the 0-1 is wrong
How do I counterattck against this?

h3 is a good start. You shouldnt really be in that position though. Be2 and b3 both seem odd to me. After the knight retreats, d3, and 0-0. Standard development really.

White to move, the best play seems to be:
1. h3 Nh6 2. d4 exd4 3. e5 and White is much better. He will chase the Black Queen away, probably double the h and g pawns, castle and then attack.

the 0-1 is wrong
So you are Black?
Why is your Queen on f6? That's a development move for noobs. Any half decent player will not only easily defend it but also drive it away gaining time and space.
Why is your Knight on g4? Similar reasoning: did you think you'd catch your opponent sleeping? It's going to get either get chased away or exchanged so that White can develop a piece. It should still be on f6.
Your pieces should be Nf6, Be7, and O-O. You've ignored solid development for an ethereal attack. This is a +- game for White.

Why would you want to exchange your bishop for the pathetic knight on h6, especially as it opens up a file in front of your king?

I would hit d4 with the pawn expect the capture, and recapture with the Queen, hoping for the excange of Queens!

1. h3 Nh6 after that, you should develop the centre because black can't properly hold it. I would go 2. a4 in order to secure a position for 3. Bc4 to gain the centre. 2. ... d5 is met by 3.exd5 cxd5 4. Bb5+ Nc6 5. a3 (so ... Bb4 6.axb4)
Black loses the ability to effectively dislodge your c3 knight and loses the centre.

I would 0-0 followed by h3 is they hadnt run away before that. By the way, your b3 move seems like a bad choice in my opinion....
There is no "counter-attack" for you. Do you know why? Because black has no attack against you. Unless you call Qxf3 mate if you move your knight an attack =P.
My suggestion would be h3 & 0-0.
Earlier in the game, I think Nd5 or d4 was worth considering (when the queen was at f6 and the knight at h6).
I think b3 to release the bishop was a bad move (Better was d3 or d4, which reinforced the central which, got the bishop ready to develop just like b3, and threatened a powerful Bg5. Not to mention d3 also reinforced the center, and d4 contested it)
I also think Be2 is a touch passive.
The opening (e4 - e5 - Nf3 - Qf6?!) is grecos attack if the game opened that way. Its a terrible opening, which hasn't been used for about 400 years.
When I lost to my opponent I wondered how to conterattack his opening. Below is the position.