Doing this now.
Get all updated vaccines including rabies, microchip. Send that information with your flight info, passport and a R
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form.
They will issue an import permit, it took less than 48 hours for mine to come in. Write URGENT- need for airline travel.
Then make an appointment with your vet 10 days before you travel for an international health certificate. They will fedex it over night to the USDA. USDA will sign off on it and stamp it and over night it back to you. Take all those to the airport and then when you land you will take your pet to the AQS at the airport and they will do a check and you pay 510 baht for the fee.