I brought my dog here in January. We flew out of JFK airport. I needed paperwork from a USDA certified veterinarian, a transit permit for China (layover), and an import permit for Thailand. Google it for more info. I paid in total about $1000. 600 for her to fly (goes by weight of dog and crate) 150 for crate, the rest for veterinary appointments, documents, and fees. I have no idea about quarantine though
I have this visa. Non-o multi entry based on volunteering. I received a stack of documents from the organization and applied at the consulate in NYC (US citizen). Got my visa the next day. Came to Thailand, got a work permit, and will change (not sure of the process) to a single entry. As long as you have the backing of an organization that knows what they’re doing, you should be fine.