Flying dogs to USA

Hi guys
I am slightly confused as I will need to fly 3 small dogs to Colorado when we move there in November but althrough I know they need their rabies jabs etc I have mixed messages about the actual transportation.
I wa under the impression from BA website that they could be booked on a flight by me and would travel in crates on board with us. Having phoned Ba they said I have to go through a shipping company!?
Has anyone transported recently?
I just want it all organized so I can relax about it!
Tabs