A very very minor nitpick of mine : I'd avoid using a Mirror Q. Given Q's abilities, I expect him to exist on many dimensions at once. Beside, you don't want a bad Q at large...
Either Q alone decided this contest (wich doesn't prevent him to blame the idea on a "Mirror counterpart" of him), or another Q in the same Continuum has taken interest in the Mirror Universe and they have decided to confront their favorite universes.
Apart from that, I like this idea. Although maybe the Qs' goal could not be to see how the catastrophe will occur, but more how both Crews will be able to work together to prevent this to happend - a bit like what Q did with Picard in All Good Things..., only this time with alternative universes instead of time.
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett