BTW - what stops Quirrell from polyjuicing as Harry, asking for private audience in Dumbledore apartment, doing quick surprise Avada Kedavra, and flying out of window? Or better yet - put Albus body to magical pouch, polyjuice as Dumbledore and run Hogward ever since. Dumbledore behaves quite strange, and rarely shows publicly, so it wouldn't be hard to do.

Dumbledore might have other methods of recognizing such a disguise. Perhaps, for instance, he can detect the approximate magical strength of a person regardless of their appearance? In Half-Blood Prince, while seeking out one of Voldemort's horcruxes, he and Harry encounter a device which is supposed to detect when a wizard passes through by registering their power, and Dumbledore notes that next to him, it's not even going to notice Harry. Perhaps while a switch like Barty Crouch Junior for Alastor Moody could slip his notice, a huge disparity like Quirrell for an eleven year old Harry would be an immediate red flag in his senses.