Being a Canadian I'd say the first thing you should do is read this
http://www.cic.gc.ca/english/immigrate/index.asp. It's the Canadian Gov's answer to immigrating. The real in depth answer to your question is no doubt a complicated one. Your cat will likely need all it's shots and verification of them. Your future employer (if they're willing) may sponser you? It's hard to just move here and live/work as it is to the USA but there's a loophole so to speak as a skilled worker/professional. I'm trying not to go on and on as I don't know the answers but I think that link will answer most of the initial questions you may have if not all.
Shame you're not coming to Ontario. That'd be one more person to ride with