Travel is living, it is living moving, so anything one wishes to do is possible. The problem is the cost, not the whether it is possible?
Can People World Travel With Dog or Cat?
Cats VERY territorial...dogs not so much. They just want to be with you...they really don't care where.
When I travel in the motorhome I take my GSD with me but, if I go by plane, train or bus I leave him with family or friends.