The queen usually stops a pawn easily - but not always. Black, with a queen against the pawn on d7, is to move here, and it is nonetheless a draw (per the tablebases): Black's king is too far away, and White's king covers the pawn on the queening square reliably.
White has a pawn on d7 and the king on e7; Black has the king on e2 and the queen on f1. The queen checks the white king about, but each time he hides on d8 or shelters behind the pawn; and Black has no time to bring the king up - the pawn queens.
The lesson: even a queen against a pawn wins not on her own but only with the king's support. If your king is far away and the enemy king is guarding a passer on the seventh rank, the result is often a draw.
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