I'm curious if anyone has any experience or knowledge about crossing the Canada/US border with your pet WITHOUT the intention of selling it?

I'm trying to plan forward to spending my future winters down south, ie: Florida. I realize we need CITES permits to import certain species and I'm curious what permit we can get to travel with our pets. This may sound crazy but just as I would bring my dog, I would bring my monitor or tegu (whichever I finally get).