Be ready for a major quarantine when you get over there  I think around 2
months
Call the airline  but I don't think you can  and IMO  is a long time
depending on where you are going from  to keep  a cat sedated

Are military or civilian?

I was stationed for two tours of duty in Japan, when I was
in the military.  Both times we lived off base, on the Japanese
economy.  Be aware, the Japanese attitude toward cats and
dogs comes as a shock for some Americans.  If a dog is found
loose, it is picked up and destroyed.  Same for a cat, if it becomes
a nuisance in some way.   Japanese authorities will do a "sweep"
of a neighborhood, if there are multiple complaints of loose
dogs & cats.  If your pet is caught in the dragnet, you can some
times save it by acting quickly, paying a fine, and acting humble.
Showing great respect for Japanese laws and customs used to
get me out of a lot of tight spots.

It depends on the airline. We didn't take ours to Japan, but we did
bring a cat from Singapore to San Francisco. We didn't sedate her. She
went in a Sherpa bag under the seat. I think we paid $75, may have gone
up now. She was not happy, but travelled pretty well. it was pretty
painless. Book in advance, airlines may have restrictions on how many
pets aboard. I think Air France is specially good about pets on board,
better check.

Other things to consider:

1. Import regs. What does Japan require by way of vaccines and
documentations?

2. Quarantine. I don't know the regulations for Japan, but you should
find out. This has three aspects: The separation from the pet (and for
the pet from the family); the care it gets in quarantine; and the cost.
You probably want to find out more there.

3. Where will you live? Are pets allowed there? Given what the other
poster said, you probably want it to be an indoor-only cat. Unless you
have a comfortable company-paid pad, apartments and even houses tend to
be quite small compared to the US or even UK.

4. If you're not moving there permanently, where are you going at the
end of your stint in Japan, and what happens to the cat then? If you
need to re-home it, it may be easier now when it's younger and in a
cat-friendly country than later on in one that isn't.

Just some thoughts.

Rupa Bose
www.rupabose.org