With a rook pawn on the seventh the defender hides the king on h1 in front of the pawn. Any queen move that takes away g1 and g2 is stalemate, so the attacker cannot gain the tempo needed to bring the king up.
This is the first of the two drawn queen-versus-pawn cases. Black's pawn is on h2, the king on g2, and White's king is far away on h8. White can check as much as it likes, but the normal winning method requires the black king to step in front of its pawn and give White a free move. Here that square is h1, and when the king is on h1 the only squares it could move to are g1 and g2. A queen that controls both squares and does not give check stalemates Black.