It seems to be a plot hole in MoR (ETA: not in canon - so the zombiehood is important) that no-one who appears on screen seems to have known Quirrel before his appointment as teacher. In particular, no-one ever gets to ask, "why is Quirrel acting like a zombie, he didn't do that when I met him ten years ago". Neither does anyone say, "I know you've been wondering why Quirrel acts like a zombie; he's been like that ever since I met him ten years ago, and here's why."

No-one is holding the idiot ball. Therefore Dumbledore didn't take a complete stranger on as Defense Professor; Quirrel must have had references.

Since the zombie-hood is due to possession/mind control (in canon), we can assume that it implies possession in MoR as well (even if possession isn't true here). Also, Dumbledore remains suspicious of Quirrel. Therefore Dumbledore must have investigated Quirrel's zombie-hood, or gotten a satisfying explanation from Quirrel himself.

Further note: Dumbledore can cast warding spells such as "no-one who wishes to harm the people living here may enter this house" (this was used on Harry's house in canon and was powerful enough to protect Harry from Voldemort and the Death Eaters in the summer vacations). The warding spells on Castle Hogwarts are described as diverse and very powerful, and if they didn't have this function already, Dumbledore would have added it (in canon he presumably was holding the idiot ball and didn't do this). Therefore we know Quirrel isn't planning to harm Harry directly, or at least wasn't planning to do so at the time he entered the castle.