As part of the enchantments protecting the Sorcerer's Stone, anyone trying to get through the chamber of keys would have to pick the right key from hundreds of flying keys, and then capture that key while flying on a broom, in order to open the door leading on to the chess room, the next challenge.
If Quirrell had wanted to keep anyone from following him past the room of keys, why didn't he simply keep the key that opened the door to the chess room? I'm willing to bet Quirrell easily figured out that Alohomora wouldn't work to open the door to the chess room -- the key was absolutely essential to move forward in the enchantments.
Furthermore, as far as I can recollect, Quirrell didn't know he would be needing anyone to get the Sorcerer's Stone until later, once he was at the Mirror of Erised, and even then it was Voldemort who instructed Quirrell to "use the boy" to get the stone. So it's not like Quirrell, I don't believe, would have anticipated needing anyone's help in retrieving the stone.
However, Quirrell surely might have feared Snape following him and interfering with him in order to thwart Quirrell from getting the stone for Voldemort. So, knowing that Snape was trailing Quirrell and watching his every move:
Knowing all this, why didn't Quirrell keep the flying key, to prevent being caught stealing the Sorcerer's Stone?