LAX to DAD with a dog

Maybe you can try LAX-SGN first. Those are big cities so bigger aircrafts are available for you big puppy.

For SGN-DAD, you will find nothing. I suggest you guys to rent a privat car. It gonna takes long long time but it's for the sake of the puppy. If you want a good private car, you can PM me. I personally know a very good driver that I always use to help transport my friends and their massive kitesurfing stuff from Saigon to Mui Ne and sometimes all the way to the North. My friends willing to pay in exchange for freedom and flexibility   

I don't know if moderation team would allow me to post a link here, but you may want to consult with Saigon Pet Clinic (http://saigonpethospital.com/).

They have a service to relocate pets, they maybe able to give you good consultation.

Also Hanoi is closer to Da Nang than Saigon... you can also try train from Saigon to Da Nang or Hanoi

I would strongly advise avoiding Hanoi, but I'd also strongly advise leaving the pooch at home.

I never saw a open dog market in Saigon, though they may exist.  I've seen several in the north, however, with Hanoi being the epicenter of this "cultural" practice.