Can white win this Q and P end game?

From this position, put black Q on the best defensive square, then it's white to move.

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

Maybe like this

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

My computer gives +6 for white, but doesn't seem to be able to find a winning strategy.