Can White win this Q+P endgame? Can white win this queen and pawn endgame?

From this position put Black queen on the best defensive square, and then it will be White's to move.

[FEN "8/1PQ3pk/6pp/8/8/8/8/3K4 w - - 0 1"]


It might look like this:

[FEN "8/1PQ3pk/6pp/8/q7/8/8/3K4 w - - 0 1"]


My computer gives +6 for White, but it doesn't seem to be able to find a winning strategy.
Black seems to be able to get away with a draw by perpetual check. The usual way for White to escape that, is to advance the pawn, or interpose his/her own queen while giving check (thereby forcing the exchange of queens). The latter is impossible because black's king is well protected. The former is impossible as well, as long as black remembers to give check from the a-file if the white king is on a8.

Your computer probably doesn't see a threefold repetition (indeed, it's possible for White to stave this off for more than 50 moves) and thinks the b7 pawn is worth almost 6 pawns because it is on the verge of queening.