No, I mean can you move them through tpa? Like if I wanted to bring my pet wolf from spawn to my house.
No, unless you buy the pet feature (which are indestructible mobs owned by you, no real function) they cannot change worlds with you.
Not sure about wolves/dogs since they would tp to their owner if far away enough... unless, of course, it would include a world change from Legacy to Rising or Vice Versa.
As long as you want to tp to somewhere within the same world, get someone to tp to you then tp where want to go. That should keep the chunk loaded and your tamed pet should tp with you.
