Besides the rook's pawn there is a second exception in queen against pawn: the bishop's pawn (on the c- or f-file) on the seventh rank. Here the stalemate idea saves the day - checking the king in front of the pawn walks into stalemate, and the tempo needed to bring the king up cannot be won.
Here White has the king on d6 and a pawn on f7; Black has the king on b3 and the queen on a1. White to move, and it is a draw (per the tablebases): the f-pawn is a bishop's pawn, Black's king is far away, and the stalemate mechanism holds the position.
In sum: the queen wins comfortably against a central or a knight's pawn, but against a rook's or a bishop's pawn on the seventh only if her king can get across. These two exceptions have to be known by heart.
Drag a piece onto the board, or click a piece and then click the squares. The cross beside the pieces sweeps every piece of that colour off the board, and a single piece can be dragged off the edge.
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It is the mating side to move. Find mate in one.
Openings, endgame positions and breakthrough studies - the set-up appears on the board.
Like a rook's pawn, it offers stalemate resources: the king hides in the corner and the next check leaves it with no moves - a draw.
By bringing your own king up: while the queen ties the opponent down with checks, the king approaches and removes the stalemate defence.
There the queen wins with the standard technique: check, blockade of the queening square, king move.
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