I'm going to go ahead and say that I think white is much better. Black doesn't really have any compensation for his missing pawn, white should be able to develop fairly comfortably and enter the endgame with a material advantage.
Note also black's disgrace of a pawn structure, no less than four islands! It's actually impossible to have more than that. 
You run into some trouble after
6. fxg6 dxc4 7 Qf7#
You run into some trouble after
6. fxg6 dxc4 7 Qf7#
6... Nf6 and black is doing fine.
I admit, however, that my comments were only made on the final position- I will look over the line and tell you if I see any improvements!
There already is a gambit in the 2. Qh5 lines, and it´s Nf6.
Ok, here's my suggestion:
Try 7... Nd4 instead of Bxf5. This will force white's bishop back (you are threatening Nxc2+) and then you can take on f5 without such a blow to your structure.
I still can't find enough compensation for your missing pawn (although someone else might be able to) but I'd say this is at least slightly better than 7... Bxf5.
I shall be updating constantly
I don't think your extended line works, as white has the improvement 9. Nf3, attacking e5.
10 d4 White has extra pawn and good position
OK, then what about e4>Nf6
OK, then what about e4>Nf6
9. Nf3 e4 is followed up by 10. Nd4 where Nf6 isn't really an option.
Ilya1975: not after exd3 en passant.
Nytik: why is Nf6 not an option, it could be followed by 0-0-0 or just 0-0?
I'm enjoying this :D
Ok, right now I'm treating your mainline as:
1. e4 e5 2. Qh5 Nc6 3. Bc4 g6 4. Qf3 f5 5. exf5 d5 6. Qxd5 Qxd5 7. Bxd5 Bxf5 8. Bxc6+ bxc6 9. Nf3 e4 10. Nd4 Nf6
(I say your mainline because I prefer 7... Nd4, as I've said, but I also note you have not yet accepted 9. Nf3 as superior to 9. d3, which I hope to prove to you now.)
The line after 10... Nf6 would run something like 11. Nxc6 Bd6 12. Nc3 where white is better.
10... Bc5 11. Nxc6 Ne7 12. Nxe7 Bxe7 where white is better.
10... O-O-O 11. Nxc6 Rd7 12. Nxa7+ where white is once again better.
Does that clear it up for you? 
Sorry, I completely missed Nxc6!
So can we now admit that 7... Nd4 is better than 7... Bxf5?! I think once we have accepted this, we might find a way to make black almost equal.
If I'm being brutally honest, though, the existing lines against Qh5 probably trump this one quite easily. (Unless we can find some strong novelty somewhere down the line!)
Ok, forget e4, what about Bd6 instead? thank you nytik. i hope i can still get this to work!
*Sigh* I see we are still trying to prove there is merit to 7... Bxf5?! I am almost certain there is not.
9... Bd6 certainly looks like a better try than 9... e4, however. I would suggest 10. d4 to reduce black's central presence.
I was looking at the position of 1. e4 e5 2. Qh5, and was getting annoyed because I hate the opening so much, I looked and looked for some sort of gambit, and finally found one. Tell me what you think!