You can ship, and it's via cargo. Last I heard (from an adopter who looked into it for 2 7 week old boys) it's expensive. The quote for her, from Cincinnati, OH to the middle of Tennessee was $250.
I'd never heard of shipping Fed-Ex, but I honestly don't trust them not to damage a package, let alone an animal. I looked it up and found this:
Live Animals. FedEx will accept inbound and outbound live animal shipments on an exception basis only, via our Flying Tigers Air Cargo Service. FedEx does not accept live animal shipments as part of its regularly scheduled service. Live animals will be accepted when the shipment is coordinated and approved by the FedEx Live Animal Desk. Acceptable shipments include but are not limited to horses (from gateway to gateway locations only). Household pets, such as domestic cats and dogs, are not accepted. For more information, contact FedEx's Live Animal Desk at 1-800-405-9052.
But I'm surprised they include rats in it.
Honestly, rats have died being shipped, it makes me weary. But if you want to pay for it...
Here's a Google search, there are some sites to read up on the subject.