Have not done this yet, but have checked into if it is possible, as I would not risk my dog stranding in China, if we had to leave. 

http://scaashanghai.org/china_pet_export_relocation.shtml

you have to match this up with the country you are going to and whatever restrictions applies there. 

there are pet relocation companies that can do all the work for you, not sure about the cost. 

in a related note. if it is a small dog, it is possible for you to carry the dog as carry on luggage on the plane, however airlines differ a lot in what they allow here, most European are easy to deal with, and all Asian airlines allows no pets in the cabin, have not looked into any US based airlines. 

I think the concept of take-away dog is somewhat different in China to many other nations.  

You will need to have rabie shots before 30 days of departure, vet health check, probably micro-chipped and government export papers. you must check the time of year. do not ship in heat. When a plane lands and shuts off so does ALL of the AC in the cabin and in cargo, also the heat sitting on the tarmac. Heat kills dogs. 

 The paper work might be a pain. I have exported cats from Canada and some times, I had to redo the papers over and over, because of silly things, writing not printing, writing outside the box, blue ink.,must use black