I don't know anything about your school, but at some schools the office of financial aid will give short-term interest-free loans to their students. Even if your school doesn't do something like that, you could try talking to someone at the financial aid office as they might have good advice about where you could get a short-term loan without getting hosed on the interest.

Also, there is a certain sketchiness to them, but you could try one of those pay-day advance places. Do they have those in Canada?

Alternatively, you could just try explaining your situation to potential landlords and see how that goes. I realize that since this is your first apartment (I assume) and you probably don't have much of a credit rating that this isn't too likely to be wildly successful, but the worst they can do is laugh in your face, right? Perhaps you can impress them by projecting an aura of responsibility and youthful earnestness?