I don't have a car as well. When I travel in a cab, I make sure I'm baby-wearing and have my seatbelt strapped on. A baby carrier is not a safety device and does not replace a car seat, but it's better than just carrying the baby in your arms because the baby might fly out of the windscreen in case of a crash. Otherwise, you could get a pram with a car seat adaptor like a Quinny. http://www.quinny.com/us-en/accessories/maxi-cosi-mico-ap/
I think many taxis in Thailand might not have rear seat belts and baby car seat is not really common in their country. If you are booking your own car, you might really consider bringing along your car seat which you can check with the airline.
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There are many car rentals which offer child seats as well. You can check with some of them. http://www.ezyrentacar.com/page/banner/detail/37/Child-Seat
Maybe take the train instead? It's very convenient and you don't get cheated. Haha. If I have to take the cab I would just carry him in my arms.
thanks