You really need to look up the import laws for the USA and the export laws for China. Each country is different and the rules depend on the country you are coming from and going to. For example, if I were to go to the USA and wanted to bring a rabbit back to Canada, there would not be much of as issue as long as the rabbit is healthy. If I was coming back form another country, the rules would be different.
Each airline is different as to what it allows. Some allow cats, small dogs and rabbit in the cabin as long as it can fit in a carrier under the seat. Most allow pets in the cargo area, but may restrict the species, breeds and times when they are allowed to travel. There are fees involved in either way, but they can vary for the airline, size of the carrier and where you are going. You would be looking at $50-200 on average.
Start doing the research now. If you need health certificates or to book the flight in advance, you don't want to find out about it a couple days before you leave.
Keep in mind that while you might be able to bring a rabbit without too much trouble, it can be harder to bring the food. You probably won't be allowed to put hay in the carrier and it might be confiscated at customs due to the possibility of parasites and other bugs. The same can go for pellets, so you should try to make sure you can get the brand in the states or switch to something before hand. Bring an unopened bag of food with you, but make it a small bag so you don't lose too much.