Whole Dog Journal has published a guide on shipping a dog by air. The article says the first step is checking directly with the airline, because requirements vary by carrier and can change quickly.
According to the article, service dogs trained for a disability can ride in the cabin at no extra charge. Family pets generally must fit in a carrier that slides under the seat. Some countries, including South Africa, the UK, and Australia, forbid pets in the passenger cabin, so pets bound for those countries may need a pet transport company.
The article says most U.S. carriers recently stopped allowing dogs in cargo holds on international flights, though many still allow them on domestic flights. It names Lufthansa as a non-U.S. airline that continues to allow dogs in the animal hold on international flights.
The article describes three options: the dog flies in the cabin or as cargo where permitted, the dog ships through a licensed commercial pet shipper, or the dog books as manifest cargo on a separate flight with the same airline. It states that the animal cargo hold is pressurized and climate-controlled. Carriers may apply "seasonal embargoes" when temperatures may exceed 85 °F or drop below 45 °F for more than four hours.
Flat-nosed (brach