@Dianna1987,
Well, any kind of mail sent through Canada Post is recognized as Proof of Address in our Library system (here in Calgary), so you might write her a letter to your address, then she can take the envelope in. I'm thinking she's going to need more than, however, so... she has to apply for something in her name at your or someone else's address.
Regarding the system, I agree. Really, she could move the day after she registered the moped, making a mockery of the whole system.