We've brought in 2 dogs from Australia and 1 from Italy as unaccompanied baggage with no problems. The is also no quarantine, but you will need a some important health docs to prove that your pets are healthy. You will need 1) a
Leptospirosis vaccination certificate, at least 21 days prior to departure Animal must be healthy and free from any sign of infectious or contagious disease and 2)
Rabies vaccination certificate. Your pet must be vaccinated at least 15 days prior to departure. Also need with 3) an
Identity certificate signed in country of origin by a registered veterinarian, describing age, breed, sex, color, etc.
A couple of useful links with info for what is needed:
Requirements for Import into Thailand &
Another useful link with info
You should seriously consider using a company that specialises in pet import/export/transport because they organise all the customs/vet paperwork, crates, flights, etc. They do all the major work and All you have to do is pick up your pet at the airport.
Good Luck
Di