Keep moving the queen so the queen is always a knight's distance away from the opponent king. When the king is in the corner, DON'T move a knight's distance, or you will stalemate it. Keep the queen there, and move your king up to block the other king, and move your queen to checkmate. I hope this helped!
How to premove to victory in a K+Q vs K endgame?

If you're reallygood, you can use advanced strategies since often your opponent doesn't play the best defense. For example:
If you can predict your opponent's moves it becomes easy.

Thanks for those comments, I like both of those ideas! Although DandyDan, I think I might try your plan when I have a bit more than 3/4 seconds on the clock.

Its 7.Qg5#, and I thought that also, however the problem with 7.Qg5 is that you can't premove it, because Black might play 6...Kh6, whereas you can premove 7.Kf5 and still have a quick mate after Kh6 and Kh5

Too many times I have drawn these basic endings with 3/4 seconds left. Is there an easy way, that the opponent cannot escape from, to premove to victory?
Use the ways above but if it takes ten moves you'll draw anyway since each premove costs 0.1 seconds

Thanks Marcus! Practically speaking I usually don't premove unless zugzwang is obvious. Often instead of premove I click-and-drag and only release the mouse button after seeing my opponent's move.

I generally try and see if my opponent is fleeing towards the back rank, if he's low on time that's a very common way to reduce pre-moving into check - often the lone King runs in a sort of backwards scissors pattern as if dodging bullets. Anyhow, if he's heading backwards, just move your King up (which also prevents ever hanging your own Q), and then just put the Q on the seventh rank as soon as he gets to the edge.

I will try that, however most the time it is me who is down on time, my opponent usually has 20-30secs (in 3min blitzez - my favourite time control!)

If you're reallygood, you can use advanced strategies since often your opponent doesn't play the best defense. For example:
If you can predict your opponent's moves it becomes easy.
Hmm...interesting, I'll have to remember that. However the knight's distance away rule is simpler for newbies, and I have never seen it done your way, but I suppose you could do that. Both work though, and I find it easier to remember the knight's distance away rule. You have to be very careful in a queen vs king ending however you play, or you might stalemate it.
Too many times I have drawn these basic endings with 3/4 seconds left. Is there an easy way, that the opponent cannot escape from, to premove to victory?