ok this is the process for someone who needsto find a passenger and it says canada, but it's the same for the US.
Exporting animals from Taiwan to Canada/US
1. One month before they are to fly you must have them chipped and vaccinated against rabies. You will be given a certificate with the chip details (registered to the owner in Taiwan) and a yellow book with the rabies vaccination details. This in Taipei city is $200 rabies $250 chip
2. Confirm with airline that animals can fly with a passenger, China Airlines and EVA air are both confirmed to be ok. However you need to call in advance to let them know.
3. Buy a crate. Must be a solid crate, not cage. Animals must be able to stand up and move around. With certain airlines some animals can travel in one crate, please check their websites for details. Make sure you also buy animal pee pads and a water bottle. Depending on size crates can cost anywhere between $1000 - 9000
4. Within 7 days before your flight you need to go to the Bureau of Animal and Plant Health Inspection and quarantine Council of Agriculture, Executive Yuan (in Taipei it is located on Roosevelt Road, Sec 4, Lane 113, No 19. Tel: 02-27387868) for the Veterinary Certificate for Export of Live animals. You will need to bring with you the Pet passports to show their vaccinations, the Rabies certificate, the Chip certificate, your passport/ID, a copy of the person who is flying the animal’s passport and flight itinerary. The Bureau weight and check for chips and then will give you the Export certificate and a copy of it. Keep these unfolded.
5. Arrive at the airport 3 hours before flight. Go to the Quarantine for live animals office usually on the first floor (in terminal 2 anyway). They will ask you to fill out a form of address of destination, flight no, passenger info, animals breed, color and weight.
6. Check in. Make sure the crate is secure and the water bottle is secure (it’s a good idea to have extra ties for this). Pay the excess baggage fee. Your animal is on its way.
7. When arriving in Canada / US
a) on the plane you are given a Canada customs declaration card. On it, check the box declaring meat, poultry, fruit, veggies, animals, etc.
b) go through customs as normal and go to get your bags.
c) when you pick up your luggage, all over-sized luggage is available separate from the regular luggage. There is a repeating message telling passengers where they can pick up over-sized luggage.
d) Now you have your luggage and your animals. Go to the exit and give the customs officials your declaration card. Because you have animals, they will direct you to the baggage inspection area.
e) If everything is ok, they'll ask some questions, check your papers, etc. You pay the fee (the fee can be between CAD$10-30 per dog'not sure about the US) and you are free to go. You don't need to fill out any paperwork.