Snapedom

Do we know Severus realized who was (literally) behind Quirrell? I thought he had to once he realized Quirrell was after both immortality and Harry, but duj believes any Dark wizard who sought immortality would also want to eliminate Harry - either because he believed Harry had the potential to be a rival Dark Lord or because Harry had supposedly already caused a major defeat to a powerful Dark Lord.

So if Quirrell was an independent threat, it is important for Severus that whatever he does to Quirrell, he remains alive and free to be able to protect Harry from Voldemort whenever he shows up. (Consider Molly's criticism of Sirius' effectiveness as godfather from Azkaban.)

Alternately, if he knew exactly where Voldemort was - he may have realized he couldn't eliminate Quirrellmort. He had a hard enough time countering the broom curse. He couldn't catch Quirrell unawares - the man had eyes in the back of his head! It was useless to poison him if he was drinking unicorn blood. In fact, once the unicorn hunt started many forms of death would no longer work.

Or perhaps Albus said something that convinced Severus that the prophecy was true, and only Harry had the ability to kill Voldemort. Thus attacking Quirrellmort directly was useless.