I flew both American and United, from the US to Buenos Aires. Try to arrive on a weekday, as animal control inspectors get paid more weekends and holidays. Upon arrival at Ezeiza, the dogs' crates came in with the luggage. I then put them on a cart and went to SENASA, the animal inspection service's office. Showed their papers, paid a small fee, and were out in under twenty minutes.
American has daily non stop Miami-BA flights, United does the same from Houston, and Delta from Atlanta.
Pets fly cargo in a special hold right under the cockpit, heated and cooled the same as the passenger cabin. It is not a large space, so make sure there is room for your dog in your flight.
The vet told me not to give the dogs sleeping pills, as they interfere with their body temperature control.
Best of luck to you and your dog....!