I got my dog in KOrea and I've flown to the US, then back to Korea with her. It is DEFINITELY doable. The important thing is that you get a health certificate for the dog before you get on the plane. In Korea you also need to get a "checkup" at the airport before leaving the country. I'm not sure how it works in Japan, but I'm sure you can do some googling and find some good information.
As far as getting the dog into the US, all that is mandatory is the rabies vaccination. What state are you flying into? Research that state's import laws to make sure that nothing else is required.
You'll find that the bathroom is your saving grace on the plane. Bring along pee pads and use the bathroom with a baby changing table. You can also take your dog out for hugs and comfort in case the flight attendants won't let you take him/her out on the plane (it's illegal to do this per FAA regs).
Make sure you reserve a spot for your dog on the plane. Most economy classes only allow 3-4 dogs per flight.
If you decide to do this, definitely read through the threads in this section. There is a lot of great info about flying with dogs.
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