okkkkk. I just flew my dog via Cathay/Dragonair out of Kaohsiung to NY via HK recently. It is very possible, but after the ordeal, I felt like I've chased my imaginary tail.
I've been in contact with the reps from the cargo department (can't fly animals as extra baggage to HK) for months to figure out what I need (for the airlines) and for weeks and months, I've been told that I need to send a scanned photocopy of my passport (ok), itinerary details (ok), get the vaccination cert. from my vet and the animal health inspection cert. from the TW govt before they "book" my dog AND apply for the HK transit permit (which they would do). I was told that booking/reserving for my dog wasn't a problem (which really wasn't, but I was a worry wart and called every possible number I got ahold of). Because there's no way I could gather both health certs. more than 7 days before my flight, I was referred to a customs booker, who also told me the same info (cannot apply for the HK transit permit or "book" unless I have those 2 certs.) which left me in a dilemma as it takes about 4-5 working days to process the HK transit permit.
I got the vacc. cert. from my vet and I took an afternoon off to go to the quarantine office* (took 30 min. tops) and sent them my docs. I then proceeded to cross my fingers and hoped that I would get the HK permit as I would fly out within 5 days.
The airline got the permit the day before.
I arrived 4 hours early as I needed to get to the cargo area. Sorted everything out and paid 24K-25K (medium sized crate and total weight was roughly 10kg). My dog was suppose to fly as cargo to HK, but as extra baggage to NY. I doubled-checked to make sure my dog was on board at HK and as it turned out, there was another dog onboard
Fast forward to arrival in NY. I was suppose to pick up my dog on the manuel/extra large baggage feed. The other dog was already picked up, but something went wrong and for some reason, my dog wasn't considered extra baggage to JFK and as I found out, he was sent to the cargo area of the airport.
So I had to find a way to get to the cargo area to pick up some documents, then go to another terminal and find the customs officer on duty to check out the docs and then go back to cargo, pay the airway fee ($50 USD) and pick up my dog.
The whole fiasco sounds terrible for my dog, but I was told he was quite calm. He seemed to care less when I finally did pick him up.
He's more of a trooper than I am.
*Note: Bring your passport, ARC, a copy of your itnerary, proof of rabies vacc. (yellow card). I was also asked for the exact age of my dog (don't think this would have applied if he was a rescue dog). I brought all my original docs and copies just in case (vet's vacc cert, microchip cert., pet "passport").