But....
The Black King cannot be compelled to play an illegal move. The game is drawn by way of Stalemate.
p.p.s. You had plenty with just the King and Rook, the extra Queen was unnecessary.
p.s. Here's a blitz game where I constantly flirt with stalemate (just having fun
) but eventually mate the King:

Surely it should be a win because there is nowhere for the king to move without being captured.
http://www.chess.com/livechess/game.html?id=183644029