No idea about Quebec, but in BC I went to an ICBC Autoplan agent and asked a bunch of questions about this stuff. You can register a car as a visitor and in BC, you actually have to get a BC licence and plates after visiting for more than 6 months if you're bringing a car in from out of province. It seems like a fairly straightforward process if you have a driver's licence from any province or state or an international driving permit. It's not letting me post links here but if you go to ICBC's site there is a FAQ for "New to or visiting BC".
Best thing to do is to talk to the Quebec equivalent of an Autoplan agent.