Half Danish gone wrong

This is a game where I ended up playing the half-danish.  I thought that I played fairly well until I blundered away a rook for a bishop (as I explain in the notes).  Then I blunder a second time by not noticing that his rook is free for the taking ... terrible play on both parts.  I end up drawing the game because he doesn't notice that I can ... What I'm wondering, is if there is something that I can do better instead of trading queens?  Or something that I can do to exploit my attack right around then?

The Danish requires sharp, attacking play by White.  After 5 ... Bb4, you should play 6 e5! d5, 7 exf6 dxc4, 8 Qxd8+ Kxd8, 9 fxg7 

7 Bxf7+! Kxf7, 8 Qd5+ wins back a pawn and strands Black's King.

9 Bd2 is too passive.  9 Nd5! is better.

13 Qf3 is a waste of a tempo; there's no reason to move the Queen.  It also blocks the f-pawn.  13 f4! presses the attack.

After 16 ... Qg5, there's no way to avoid trading Queens without losing material.  At that point, your attack is more or less finished.

Going back a half-move, 16 f4! gives Black problems, as it threatens f5 and also keeps Black's Queen out of g5.  Black has no good way to counter f5 and practically has to give up a piece to stop White.  

@ Ponnupazoozu you're right, that does look a lot better there.  I like it.

@TomBarrister Wow tom, thank you so much for the analysis.  I'm looking over everything that you said and I like a lot of it.  I normally do 6. e5 there, but I'd done it already so many times in the past that I wanted to try something a different.  I had just recently reviewed a full danish game by a better player than I, that brought the knight out and sacced the e4 pawn and turned it into an awesome checkmate.  My play here was trying to emulate this game (http://blog.chess.com/meanpc/danish-gambit2) as closely as possible.