Hi,
We moved our cat to Germany 7 years ago & back to the U.S. a year ago. With Germany, we just needed a health certificate dated within 10 days, as well as of course, up to date shots. I'm pretty sure with Japan things are a bit more strict & a Quarantine is involved.
Here is a link to the CDC. You could also try calling the airline you're going to be flying with to see if there are any other requirements. Some airlines are more strict than others. I also know there is a policy that says if the weather is over or under a certain degree at any point in time during the journey, the animal cannot fly (underbelly of course - does not apply to carryon).
Best of luck!
Also, here's another link I just found:
USDA website on importing pets.
Also:
FAQs from the CDC on importing pets.