First, be sure your dog meets the requirements established by SAGARPA-SENASICA for dogs entering Mexico. Link to Consular Services page on importing pets to Mexico. You’ll need to have vaccination and health certification from your veterinarian at minimum, and I’d recommend if possible a letter in both English and Spanish, and personally would recommend notarization. (Many in México are still favorably impressed by raised lettering, stamps, etc. and in México notarization is actually much more formal than in the US, requiring a specially certified lawyer and of course more impressive.)

Id check with AA for instructions on arrival at CUN. You’ll want to get the dog in an expeditious manner given the heat, I suspect.

According to Volaris (airline), your dog will be delivered in its cage at the baggage carousel.