Q+P vs Q is more common than Q vs P, but it receives less coverage. That's probably because it is complex, and in fact humans knew little about this ending until the advent of tablebases revolutionized its study.
Rook and Knight pawns usually draw if:
Bishop and Central pawns usually win unless
- the defending king reaches the promotion corner.
- the defending king reaches the corner opposite the promotion corner.
- the defending king gets in front of or very near the pawn
The weaker side should get their king to a drawing zone, perpetually check the attacker, avoid queen exchanges, and avoid pawn advances.
The stronger side should prevent the defending king from reaching a drawing zone, move their king to the same rank or file as the attacking king to threaten a queen exchange, centralize their queen, and advance their pawn.
In the above diagram, both kings are on the same rank, so Black must be careful to avoid queen exchanges. 1...Kc3?? 2.Qe5+! Qxe5+ 3.Kxe5 +-
And that's what you need to know in a nutshell. :)