United accepts small pets in the cabin for a per-flight fee and coordinates larger-animal transport through cargo rather than as checked baggage on international itineraries.
In-cabin travel
Allowed Checked (hold) travel
Not offered Manifest cargo
Allowed IATA Live Animals Regulations: IATA LAR (PetSafe cargo)
Comparing carriers for a route?
Airline pet rules stack on top of the destination rules. Check both before you book.