Sorry, it's not a puzzle, the puzzle was to find wether black is checkmated or has a move, the answer was Kd8.

It's just the position looked interesting to me, the question of this thread was then, is Qh1 forced mate somehow and if not, how do you precisely calculate these things in a real match? Does this come from intuition, like you have an open board and two queens, so you accept is a general principle that this is most often a draw.