Flying Dogs to and from Mexico (Cabo Airport)

We've driven down to La Ventana several times but this year we are thinking of flying ourselves and our medium sized dog. We are investigating Alaska Airlines since they have a one stop (no plane change) flight from Oregon to SJD. I’m aware of most of the documentation requirements (health certification, rabies, and etc.) but I’m wondering if I can get a sense from someone who has actually flown a dog to MX about how safe or risky it is for pets to make the trip. Any feedback, tips, or suggestions you could provide would be greatly appreciated.

Thanks

Patman