Put simply, they do not. According to their service guide document, FedEx will not accept household pets — no cats, dogs, birds, or hamsters.
Note that FedEx Express does occasionally ship livestock, fish, or zoo animals. However, these are rare exceptions arranged on a case-by-case basis. As part of their regular service, no live animals are accepted for transport.
Generally speaking, it’s not the best idea to rely on general-purpose delivery companies for animal transport anyway. Instead, try finding a specialized pet transporter and arrange the move by dealing with them directly.
For more information on dealing with independent transporters, consult our Help Center or email CitizenShipper directly.
Stay safe, and happy shipping!