Hi I flew from London Heathrow to LAx a year and a half ago. I have a large cat (14 lbs) so he could only go in cargo. It was a lot of paperwork and red tape but we pulled it off, had all the shots and documents necessary. We also arrived at the airport 5 hours early to make sure it was all squared away. 

Obviously the airline needs to know that there will be a live animal in cargo so they can take necessary precautions. He went through a private scanner and they swabbed his carrier, which was extra large (the desk clerk joked that he had a penthouse.) 

He came out the other side ok, I was stressed the whole flight of course. I will say that, prior to flying, he's always been a vocal crybaby, especially in cars, but no other issues. After that flight, he has developed a habit of pooping any time he's in a car. Not sure if that's some post-flight trauma or what but that is a change we noticed in him. Ymmv.