Most airlines require a health certificate from the vet, but aren't specific about vaccination requirements. What is required for the heath certificate is generally determined by state law (where puppy is being shipped from).
Each state has their own rabies law. You will have to abide by the laws of your state. Most don't require a rabies vaccine vaccine before 4 months, but there are a few that require it at three months, I believe.
You can check your state's rabies law here:
http://vaccines.dogsadversereactions...RabiesLaws.pdf
This is a good article about flying with a pet. It has links to the various airlines with specific requirements.
Article: Shipping Your Pet