kings gambit vs immediate queen h4 check

You have no reason to move your King!
Queen Check is just bad!
However, Black does have a very dangerous trap line.
I have played the line as Black.
If white messes up, They can lose on spot to the Trap.
If white plays correctly, They will end up facing the Fischer Defense which was the line Fischer created which was said to refute the Kings Gambit.
The move 2…d6 is a Trap.
The best move for White is Nf3, but some players mess up and try to take the e5 pawn.
If you take e5 pawn, Than the Queen check line is devastating and Black wins!
All these lines are considered winning for Black.
Best move for White is to avoid falling into the Trap.
Best play the line often goes like below:
At this point, The Trap line has transposed into Fischer Defense and White has 2 moves they often play Bc4 or d4.
Some database doesn’t call above position Fischer Defense, but if you do normal move order.
You reach same position!
Same position white to move with either Bc4 or d4.
Bc4 - Black plays h6
d4 - Black plays g5
I could explain why above moves are played, but I don’t want too. It is to much information and variations which would need to be discussed in order to explain it correctly. Their are books written about it.
Short Hand Explanation:
Black is trying to keep f4 pawn.
White Gambit f4 pawn which is why line is called Kings Gambit to begin with. Obviously, white wants to get pawn back and doesn’t want Black to be up 1 pawn.
So yeah - It’s like opening up case of cans full of worms. I just can’t be bothered discussing it.
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Anyway, your original question was about Queen Check which has nothing to do with the other moves.
I answered your original question because it has very simple answer.
There is nothing for Black!
After g3, they have nothing!
All Queen moves can get Queen captured or something. They have nothing.
All the squares are protected so they have to run away and their check was waste of time.
That would just be terrible position for Black.
I appreciate the feedback tygxc and Ralph. Those variations really helped me in getting the knight back into the center and starting to develop the middle. Before as you both mentioned with the pawn move that was passive it basically kept that knight stock to the corner not doing much, and moving pawn h4 instead of h3 also prevents the queen check as the rook is a threat.
I'll post one last question about this opening as I think beyond this its just my skill that needs improving. Below is an example where I did better in the opening using your suggestions. I believe the first 10 or so moves were all book moves. But still, it seems like most of the game ends up being played in the right most files rather than the center, with the pawns creating a promotion threat and the queen having that file to always threaten a check. I guess im just asking, since kings gambit is about center control, it seems like for me at least, it does the opposite where my energy is diverted to preventing checkmate and promotions rather than attacking myself. You can see in this game how the morphy bot beats me with 2 brilliant moves per the analysis. I'm not really sure what I could have done different in this scenario though as I never really had open opportunities to attack.
@3
The move 4 h3 is passive. Better 4 h4 or 4 d4 or 4 Nc3.
The moves 4...c5 and 5...Qe7 are no good. Just 6 Nc3 threatening Nd5.
10 Na4?? is a blunder, just 10 Qd1 or Qd2 is good for white.

I completely agree with @tygxc there. 4. h3 doesn't gel with the gambit mindset. Giving up a pawn in order to then defend against an opponent's possible pawn pushes isn't the ideal.
To expand a little, 4. h4 looks to try and prove that Black's advanced Pawns will be weak and that their advance will open up his King to attack eventually. 4. Bc4 looks to play in the centre and/or down the f-file (sometimes sacrificing the Nf3 or even more material) using the initiative while Black can try and count the extra Pawn as a static advantage or a weapon to become a K-side pawn storm. 4. Nc3 has elements of both (White often plays in the centre using the initiative but can throw in Pg2 -g3 to attack Black's pawns). Some samples of the sorts of interesting play that might arise...
I appreciate the feedback tygxc and Ralph. Those variations really helped me in getting the knight back into the center and starting to develop the middle. Before as you both mentioned with the pawn move that was passive it basically kept that knight stock to the corner not doing much, and moving pawn h4 instead of h3 also prevents the queen check as the rook is a threat.
I'll post one last question about this opening as I think beyond this its just my skill that needs improving. Below is an example where I did better in the opening using your suggestions. I believe the first 10 or so moves were all book moves. But still, it seems like most of the game ends up being played in the right most files rather than the center, with the pawns creating a promotion threat and the queen having that file to always threaten a check. I guess im just asking, since kings gambit is about center control, it seems like for me at least, it does the opposite where my energy is diverted to preventing checkmate and promotions rather than attacking myself. You can see in this game how the morphy bot beats me with 2 brilliant moves per the analysis. I'm not really sure what I could have done different in this scenario though as I never really had open opportunities to attack.

2...Qh4+ is actually playable. The follow up, 3.g3 Qe7!? is the Keene defense, named after the British GM Raymond Keene. The idea is to exploit the e4-h1 diagonal that's weakened by the move g3. The main line is:
Here's a miniature between a couple of 2300+ players:

@rifreef it looks as if you do not have a lot of access to books on the King's Gambit, and some lines are long and tricky with many tactical variations to know about. If you can get/afford a copy of John Shaw's "The King's Gambit" (Quality Chess, 2013) that's very comprehensive and is my own go-to for current theory. The older book by Neil McDonald or the one by Joe Gallagher are good too but are no longer up to date (the latter does not claim to be comprehensive, White's lines covered are the ones the author recommends). In the game you played, the natural-looking 9. O-O is probably the strategic mistake. Castling that soon means Black can get straight on with preparng ...Qxh4 and seeking to have at White's King. Your game briefly transposes into a game from 1991 which demonstrates how bad things can get for White...
Judging when to castle and when to defer it (and occasionally when to tuck the King onto d1 awhile instead) in these lines can be challenging. There are reams of theory on the position after 8..., Nh5 but one main line (given in the John Shaw book) runs as follows. At the end of the line, White has several move 14 choices such as Bxf4, Qd4, b4, and b3. Shaw seems to prefer 14. b3.

PS @rifreef I don't usually play 4. h4 but I had a look at the Morphy bot's responses. In that last line I gave in #8 it played 10..., f5 and after 11.Ng5 it went ..., Qe8 which I can't find mentioned in any books. I died badly having picked the wrong plan; with 12. Qd3, Ng3 and White is in trouble. Not enough time available in which to play Kd1 and Re1. On reflection, after 12. O-O instead I think White might have at least sufficient compensation for the Pawn. Ideas like playing Ne6 are in the air and generally if White can chisel open the a2-g8 diagonal it's usually a good sign.

@tygxc Now that is really interesting to me. I'm coming back after a quarter-century layoff from chess and only recall there being the following two precedents for 6. Nxg4 (the second is a fragment; which the Older Sources usually conclude with some comment of the type that Black's pieces should be better than White's Queen). Have there been developments or re-evaluations in the line after 6..., Nxe4 since I was last a properly active player back in the pre-computer-analysis Dark Ages? It's a line I'd relish hearing had been rehabilitated. [Edit: I might have answered my own question now. An analysis bot tells me that in the second game 14. Nc3, Bxh4+; 15. Kd2, f6 is stone cold 0.00 equal]

After the above moves, Black has a choice on few different moves they can play.
The main continuation which is considered to be the best way for Black to proceed is by giving white back the pawn. Black plan is to let White waste time recollecting the lost pawn while they try to get lead in development.
So the normal line goes like below:
- The move 5…d6 opens up Black Light Square Bishop so it can be developed in future.
The move also kicks White Knight forcing it to go where it wanted to (Recollect Pawn)
- The move 6…Nf6 tries to develop another Black piece and creates a Fork.
Black is attacking Knight on g4 with Bishop + Knight (White is only defending it with Queen).
Black is attacking undefended e4 pawn.
White could try retreating, but most players don’t because it waste more time with Knight and puts Knight on very passive square (f2).
The main move is to trade and Black recapture.
- After all the dust has settled, White regain being down 1 pawn. Black manages to trade extra pawn for temporary piece development lead which isn’t bad trade.
The main line theory does continue further!
After the above moves, Black has 2 continuations.
They can do Queen trade or they can play Bg7 and see if White wants to trade.
Now, the reason I explained all the above is because in order to understand the other lines. You sort of have to understand the main (best) line.
The best line with the best plan for Black is to give back the pawn and let white waste time getting back the pawn. Meanwhile, Black is trying to be cleverly steal away White development so that Black gains development lead.
Its important to understand because the other lines are going to try and keep extra pawn.
The problem is they don’t have enough fire power to keep extra pawn because White has lead in development. They haven’t stolen it away!
White in the other lines will often have compensation.
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The other moves you will see in above position are:
- Nf6
- h5
The Nf6 line doesn’t defend g4, but it attacks e4. It creates a trade which is fine for Black because they are still up 1 pawn.
The h5 line defends g4, but it doesn’t develop a piece which causes Black to get further behind in development. White often gets good game by trying to attack f7 and play in center.
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Their is something which I want to mention which is very important!
I have had a lot of King’s Gambit friends over the years.
I, personally, have never played the King’s Gambit.
I mainly played against it with Black pieces.
I had to learn what White is trying to do with White pieces so I could have better understanding of how to defeat them with Black pieces.
This is why I sort of know some of the White ideas and plans.
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However, the important thing I want to mention is all my King’s Gambit friends eventually stopped playing the King’s Gambit.
I asked them all why they quit playing it and they all gave me same answer!
Their is 1 chess line which the majority of my friends hated playing against!
They all stopped playing the King’s Gambit because of this 1 line.
The above line is in my opinion the King’s Gambit Killer!
It has retired more King’s Gambit players vs. any other line.
It’s not even considered to be a strong line for Black.
The position is like even or something. The line is nothing special, but it seems to cause so many King’s Gambit players massive frustration or annoyance because they seem to quit due to this line.
I have never played it as Black.
I have also never played the King’s Gambit as White.
I really don’t know why KG players get upset to the point they quit playing the KG.
I’m telling you this line is the cause.
Every KG player I talked to says they quit because of this line.
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I AM TRYING TO LET YOU KNOW!
Your putting a lot of effort into studying the KG line.
Your playing against the bots.
Eventually, your going to want to play vs. humans.
Your going to see this line a lot and if you don’t enjoy playing against it.
Your probably going to quit the KG like my previous friends.
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I like give people a heads up.
Maybe, you already know and if that’s case you can just ignore this part of my post.
BUT some people don’t know!
I am mentioning this as well because it did sound like you was having doubts.
It’s perfect fine to have doubts!
Their are over 100 opening in chess.
‘Some, you will hate.
‘Some, you will love.
‘It’s part of the enjoy of chess! Finding the lines which suit your play style.
Thank you to everyone for your well thought out posts and resources! I will study the above mentioned reading material and the lines provided have helped a lot. I wouldnt say I am attached to the kings gambit, but more, I am trying to learn to play in general and felt like its making me think about all the possibilities, and, it is exciting and interesting to play. Thanks.