Had such a situation recently and could not find a way to force mate.

I am phone and cannot post the board (does it even matter?) but it was pawn race with knight player promoting first and no promotion checks on either side. Seems like the single queen player can force queen exchange or keep checking or allow queen sac for stealmate ://

I'm not sure if it can be achieved in some forced sequence, but maybe the knight can fork king + queen after the lone queen interposed (proposing exchange) for a diagonal check.

According to Mark Dvoretsky in his Endgame Manual, "A queen and a minor piece cannot, generally spreaking, win against a queen. But exceptions are not so rare with this material..."

So I guess in practical terms, a draw is the most likely outcome, but a win is possible.