I played this game mostly last night. It wasn't a live chess game but we were both online for a while, so it might as well have been a live game with a long time limit.
Fastest game I've won yet
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7...c6 would have been a good move for Black. 8 Qe5+ (not Qh5, because Nf6 develops a piece for Black while gaining him a tempo) followed by 8..Ne7 9. Bc4 you seem to be well developed and have good attacking prospects in that situation. Your c1 Bishop can come out to play, while your KRP can storm Black's castle should he attempt to do so.
After you played 10. Qxa7, 10...d5 would have been an interesting try for Black to get back into the game actively. He gives up a pawn but gets some good counterplay. 11. exd5 Bg4+ You've got to play pretty precise defense. 12 Be2 Qxg2 13. Re1 (Not Rf1 here because Qxf1+!). This seems to be Black's best play after losing that Rook.
Prompting the Queen trade was perfectly timed. You needed to get the Queen back into the game where it mattered, and he did well to decline. exd5 then gave you a commanding advantage. On his last move, 16...Bxd3 might have been his best try, and even after 17. Qxd3 Re8 then his slight lead in development wouldn't have overcome your material advantage. Attacking piecemeal right away wouldn't be safe, but you'd need only consolidate your position (something like 18. c3 followed by 19. Kc2 and 20. Bd2). Then you're mobilized and he can't stop you for long. Well played, you took advantage of the opportunities.