Help with a king's gambit study?

What would be a good continuation here? Also, if one of my move are inaccurate, feel free to let me know.

e4 e5, f4 exf4, Nf3 g5, Bc4 Nc3, d4 d6, c3 h6, 0-0 Nf6

8.Qb3 is good.

Actually Bc4 is a bad move and black has no trouble what so ever he stands slightly better. The only way to avoid getting in a slightly worse position is 4. h4 and ofcourse that only leads to an equal but very complicated position.

And Qb3 can be considered a blunder as after Qd7 black is clearly better

he asked for a good continuation from this line.

I'd try the fun-looking e5!?.  Black is underdeveloped, and his king is in the middle of the board.  Black should have played Bg7 earlier, but e5 brings the fight to black before he's ready.

e5 is even worse than Qb3 because after dxe5 white cannot even take back because of Bc5 and Ng4. So he is 2 pawn behind with very little compensation.

If you want to play kings gambit play it with 4. h4

The diagram position looks sub-par for white. 8.Qb3 is nothing, Black can play 8...Qd7, as well as 8...Qe7 (probably even better) as well as the cool-blooded 8...Na5!? which merely calls white to show his bluff. White can get the pawn back, but this will destroy his attack and Black will have the bishop pair and pressure against white's center. Sample line: 8.Qb3 Na5!? 9.Bxf7+ Ke7 10.Qa4 Kxf7 11.Qxa5 Kg7!? intending ...b6 and ...Bb7. Every sane person on earth would take Black here without a second thought.

The suggested 8.e5 is fun indeed, but for the wrong person after 8...de5. Factly, white is probably lost already.

4.h4 is indeed the only move to be seriously considered for white- unless you are playing against a woodpusher. But then you could also employ (instead of the king's gambit) 1.Nh3 with a crushing advantage already.