Instead of adopting, why not check into fostering a pet?
Am I allowed to adopt a pet in Australia's animal shelters despite being a foreign student (and not a permanent resident)?
I would think that you would need a permanent residency. I know you can just go and buy a guinea pig from the local pretty store, but if you wanted to adopt from the RSPCA, you might need proof of residency. You'd have to look into it more.