We, the readers, know directly about lots of evil things Quirrell has done (e.g. kill Skeeter, break Bellatrix out of prison). We have also used this knowledge to guess at nefarious motives in other, less obvious, cases: like guessing that he was trying to dement Harry, or guessing that he is Hat&Cloak, or guessing that he is constantly manipulating Harry for his own ends.
Dumbledore has access to none of this knowledge. To Dumbledore, Quirrell is an exceptional teacher of Battle Magic who has the interests of the students at heart. He does not appear to take part in politics, with the exception of his pro-unification speech after the battle in the lake.
Dumbledore thinks that Voldemort is “less than spirit, less than the meanest ghost.” The ancient tales he found speak of “wizards possessed, doing mad deeds, claiming the names of Dark Lords thought defeated.”
The two pictures don’t fit together — Quirrell is not doing mad deeds nor claiming the name of the Dark Lord. It’s true that Dumbledore knows Tom Riddle was exceptionally brilliant, but I don’t think it’s idiotic of him to not guess that maybe the old tales of past dark lords only told of the stupid ones, and that Riddle’s style of possession would be different.
When will Harry tell Hermione the truth? I feel like he should insist she learn occlumency first.