Alternatively, Voldemort has tried killing Harry, it didn't work, so he wants to eliminate Harry as a potential obstacle through other means. If Harry's soul is sucked out (or whatever the Dementor's Kiss does, actually) then he is still alive technically but not an obstacle. It's worth a shot as an alternative approach to just trying to kill Harry over and over, which is what canon Voldemort tries to do.

Also, and this can't possibly be Quirrell's reasoning, but it's still an interesting thought: the MOR version of The Prophecy says that "either must destroy all but a remnant of the other". If Harry is subjected to irreversible Dementation, all but a remnant of him is destroyed.