I bought my motorcycle from a guy in Quebec. It was a no brainer. I just had to have an Ontario safety done to register it.
Probably not relevant to this case unless you are trailering the car but there is a weird law in Quebec (yeah, surprising) that if you are towing something with wheels on a trailer they want to you buy some sort of additional insurance from SAQ to cover the wheeled vehicle in tow, (not the trailer) in case it falls off.
I found this out a few years ago when purchasing a motorcycle in PQ.
I think it's incredibly stupid so I always just take my chances and tow anyway, but apparently I could be fined.