My family went pet-less overseas and then got a dog in the Middle East. We named him Morgen. He was a Dalmatian. And when it came time to move from one overseas location to another, he was a hungry, nervous, piece of freight. All things considered, having a large pet is not very compatible with expat life. You can take your pet with you, but you must anticipate complications.
Pets that travel as freight (as most do) are subject to all the same conditions as luggage, including getting lost. Morgen once went to Detroit when we didn’t. We got him back a day after our arrival. The sedatives prescribed by the veterinarian (another consideration) had worn off, and he was a wreck. And then there are the entry procedures and even possible quarantines to consider. A few countries make it very hard to bring in a pet, and the information on procedures for importing an animal can be hard to obtain outside the country.
I’d be interested in hearing your warnings, anecdotes, and advice about travelling with pets.