I recently brought my 2 cats from new york.. it was very easy.. I can tell you about the US to BA part. What I dont know is what you have to do to bring the pet back in..
you have to take your dog to the vet and get a document that is from the USDA that attests to the animal's good health..
you have to send that document to the local office and they will certify it and send it back to you. there is a small fee for that.
Each airline has it's own rules. I can tell you about American. They will NOT let pets travel in the cabin to south america. PERIOD. And there is a rule that says that the temperature cannot be above or below a certain number in the departing and arriving city.. (for New York to Buenos Aires that means we can travel with pets only in the spring and the fall). It was explained to me that this is in case the animal is left on the tarmac for an extended period of time, not because of the temperature in the cargo hold.
You have to book a ticket for the pet. and I would speak to more than 1 person at the airlines, because I found that many airline employees were not too familiar with the rules about pets. Although I did find that once I spoke to the right person, I was quite impressed with the care they take with the animals.
Your airline will notify a corresponding person in BA that you are arriving with an animal.. Once you clear immigration, and after you get your bags and your dog, you will see a veterinary person who will take your documentation and take a quick look at your pet. That's all there is to it.. There is no quarantine... nothing.
My vet absolutely said don't drug the cats.. if there is a loss of cabin pressure and they are drugged up, they wont be able to adjust their breathing.
I wouldnt worry too much about sending the animal in cargo.. my cats did fine. It is pressurized and heated. They are happy and healthy and loving la vida loca.
Now if they would only learn Spanish.
hope this helps. Please feel free to contact me if you need to know more.