The expense of shipping dogs can be fierce (depending on the size), and some airlines don't ship animals at all during the summer months, which could hold you up coming or going. A friend of ours was moving back to the states from a military base in Japan, and had to arrange transport for her large dog (lab) and couple of cats on a commercial flight - it was over $700, just for the dog. I believe small dogs are permitted in the cabin, but you'd probably still have to pay for a seat on which to put the carrier.
Then you'd have to consider vaccination requirements and quarantine issues both coming and going. When my sister-in-law moved to Hawaii, they had to quarantine their dogs for four months. That's four MONTHS of kennel costs. Probably they wouldn't be as expensive in Thailand, but it kind of defeats the purpose of having your pets with you, if they spend half their time in a kennel.
Finally, you'd have to make sure that you stayed in places at which dogs were welcome. I've never seen dogs in hostels or guest houses anywhere we were in Asia, nor in any in Europe. It would seem to limit your options.
We have lived overseas, in several different countries, for two and three years at a time, and have met many many other people who do the same thing. We're in the military, and the military usually does move pets with families, but even so, many of our friends opt to leave their pets in a loving home back in the states, just to spare all of them the headache, discomfort and upset of a short term move. If you were going to be moving there permanently and had a stable home in which to put them, then it might be worthwhile, but for a temporary move (and if you do some traveling around in country, you'll be fairly unsettled the whole time) it's probably fairly impractical and stressful to bring pets along too.