Qc6+ is a draw (by tablebases) because the king is pushed back to e7 and this allows the white king to get back to the pawn with Kxa6 and Kb5 (Black cannot trade queens with the king so far away).
Q+P vs Q is extremely difficult to play correctly and relies a lot on concrete calculation. There are probably more useful endgames to study.
This looked to me like it was a draw although with more chances for white to go wrong than black to go wrong.
It seems that even Stockfish is confused by this position and thinks the same move is both better and worse than itself:
I read in GM James Howell's book "Essential Chess Endings" (emphasis mine, ... to indicate edits)
"One type of ending that does occur frequently (usually out of a pawn race in a king and pawn ending) is queen and pawn against queen. If the defender's king is in front of the pawn then he should draw easily...
More interesting and common are those positions where the defender's king doesn't manage to blockade.
For the superior side...winning the game involves a repetitive and laborious process: a long series of checks will have to be evaded...
Computer databases can now play these endings perfectly and have been used to point out error after error when grandmasters have played them.
These endings often drag out for 50 moves or more."
In the position I spent a long time calculating lines beginning with both Qc7+ and Qc6+ and thought that they were both draws but Qc7+ gave a small possibility of ...Kd5?? allowing Qc6+ Kd4 Qb6+ winning the Queen and the game. I didn't seriously consider either Kxa6 or Qd8+ so apparently went wrong on the first move.
The game ended in draw by agreement (after the position repeated once) but the final evaluation was -3 so apparently completely winning for black but neither of us saw it.
I want to learn more about these kinds of positions. If even Grandmasters are misplaying them I am not too confident that I can play these right but I want to improve as much as I can.
Can you see a forced win for black here? Or a forced draw for white?