So.

Perenelle is an evil, selfish (according to Quirrell) Dark Witch of unfathomable power, who trained Dumbledore and kept him afloat in the war by parcelling out ancient knowledge whenever he fell behind Voldemort, and held the Philosopher's Stone, which she gave to Dumbledore to guard after Quirrell faked evidence of some way for someone to find it.

...What?

Why on Earth would perhaps the most powerful witch alive give one of the most powerful artefacts in existence to her apprentice to guard? Why not guard it herself? Even if the Stone could be found, why would Hogwarts be safer than her sock drawer? There are potions that affect sleep cycles and she can self-Transfigure, so she need not sleep.

Why would she allow the Stone out of her control? Could the Mirror itself just be a decoy? Perhaps Quirrell really is the most powerful wizard alive and Dumbledore's ownership of the Elder Wand places him above Perenelle on the power scale, but he can't guard the thing 24/7 (again, unless the Mirror is a decoy and the Stone is in Dumbledore's pocket).

I suppose this depends on just why Quirrell needs Harry to penetrate the Mirror, but it strikes me as odd why Perenelle would surrender her immortality to Dumbledore.