We moved our cat to Vietnam - I know not a dog, but ....
Checked with the various airlines to see who would let us bring the cat - in the cabin - and except for the time in transit in Japan (when the cat was "in an undisclosed location"), he traveled with us in garbage class. A Finnish acquaintance moved his dog back to Finland from Hanoi last month, in order to beat the new EU microchip rules, but I don't know the details on that.
Another thing to keep in mind is that there is no expat vet here in Hanoi that we are aware of. We have not found the local vets to have anywhere the "petside manner" one expects - we have tried 3 in the last 2 years for "Rover" and still are interested in hearing any recommendations.