There are a lot of pets checked by air. I haven't heard that trains can transport them.
Besides, if you don't go back for the New Year, even if your pet arrives first, no one cares ... it's better to take it with you everywhere.
Or go directly to the pet store in your current city and find someone to take care of it for a few days, and then come back to pick it up after the Spring Festival, which is not more expensive than the freight.