1.e4 e6 2.Qf3 b6
Develop the bishop to b7 and white's queen will be exposed on the diagonal. This diagonal is very weak and when you play b6 and e6, the white's light square bishop is fairly useless. In addition, you want to aim for a d5 break. Black should have equality and maybe a slight advantage.
i began a thread a few days ago about responding to irregular openings. the advice suggested playing an opening that makes the opponents move a mistake. so for example, 2. Qf3 is blocking the knight from it's normal f3 square, so perhaps you could try to work towards a position in which your opponent should be playing Nf3 and therefore blocking that square with the queen could lead to some problems for your opponent.
Perhaps it's better to accept that white hasn't neccesarily made a 'punishable' mistake and is simply wasting time. A good knowledge of your plan will make it easier :). I'd suggest essentially continuing with natural moves, his Qf3 will refute itself soon enough. Moves like that aren't neccesarily all that bad though, I've seen IM's play 1. e4 e6 2. Qe2?! vs. other masters and win... it's just a clever way out of theory.
1.e4 e6 2.Qf3 Nc6 (threatening Nd4) 3.c3 d5 (threatening 4...dxe4 5.Qxe4 Nf6) 4.cxd5 Qxd5 (as white cannot play Nc3) 5.Qxd5 exd5 6.Bb5 Bd7 7.Nf3 0-0-0 is an example continuation from database.
Qf3? Wtf?? The only reason to move your queen on the second move is 1. e4 e5 2. Qh5
Nakamura style! I'm not kidding! It's an awesome opening!
Can´t we play a game in that line Rich? Please, I´ll play as white, 1.e4 e5 2. Qh5 Bd6, please?
Those ratings aren´t true, and seeing as how black is down more than 10 material in move 10, that game is hardly a motivation for 2. Bd6 is it.
wow Tricklev is look like we got a heatwave on these early queen opening have we ?! 
This might be crazy but what about 1.e4..e6 2.Qf3..d5
Someone over 2500 played Bd6! But I think Qe7 would have been better than Nh6.
This game is a joke, these are beginners.
Easy! Play Nf6 and Bc5, go for a Traxler :P
giving advice on current games is illegal
What about c5?
So I play the French Defence against a guy rated in the 1500's and he responds with 2.Qf3. I know it has to be unsound to move the queen here on the second move of the game, but I don't know the best way to make these 2.Qf3 types pay what should be their premature aggression.
How do you respond to 2.Qf3?