An interesting position, and I don't see a better move than 1.h4, but I don't think it is necessarily a clear winning move for white after 1.....Qg3 2.Rf3 Qh2+ 3.Kf2 Rb6.

I am having a difficult time making anything of this. White can buy a move with 3.Kf1 instead, but black will still check from h1 then take at h4 with check if the white queen leaves the 4th rank. White has some pressure, but I don't think it is decisive by any means.

1. h4 - when all else fails, attack the Q. Well, on a more serious note where can the Q go?

1...Qg3 2. Rf3

1..Qh5 2. g4 Q:h4 3. Q:g6+ and mate next