My brother relocated to Australia in 2018 with his wife, Claudia, and dog Geronimo. They used a service where they gave Geronimo to them in LA, and got him back in Australia after he cleared Quarantine. They handled all the custom paperwork and you as the owner would have to get him cleared to fly by giving your pet a certified physical within 7 days of flying. They also sent pictures everyday of his status while in transit and quarantine. I will see if I can get the name of the company and post it here.