I used to have a pet rat and loved it, but before getting one as a traveler, I would consider:
1 They pee and poop where they like. Someone above said hers was cage-trained and that's great, but I don't think you can count on it. In fact mine didn't like her cage at all. It was hard to get her through the door, so she didn't want to go back there to pee either, I guess.
2. It may be against the rules (perhaps even in some places against the law?) to take a rat or other potentially destructive critter into some places, be they public or private.
I'd stay away from pets that authorities might find troublesome.