I do assume that Dumbles operates on extensive access to prophecy as well as his own plotting, so it's possible that he gave Harry the cloak because he know this is required even if he doesn't know why.

One possibility I've been kicking around is that Harry will destroy this world with Quirrell in it (and the stars themselves) to take out all of his horcruxes, but will transport himself and much of the rest of the world into a mirror realm first. The mirror and it's contents will survive, and Quirrell will be left out of the mirror world escape because the cloak is covering him. I can't really make the details work in my head, but it's a scenario where the cloak becomes a liability to Quirrell.