The following information re: traveling with your cat, from American Airlines will be helpful:
Specifically, flying to Japan:
"Due to USDA restrictions that an animal be offered water every 12 hours, checked pets must be booked on flights where the actual flight time is less than 12 hours. The Japanese government also requires you to notify Japanese Animal Quarantine Service at least 40 days prior to arrival. The pet must be fitted with a microchip. Additional documents and certificates are also required. Contact Japan's Ministry of Agriculture, Forestry and Fisheries for full information. Also, PetTravel.com has information regarding traveling to Japan. CLICK HERE"
As you can see, your cat will need to get a microchip from her vet, for identification purposes. You can get further information re: vaccination requirements (I think you're ok with those, but the time of the vaccinations, before leaving, is important), and quarantine rules by clicking on the link at the site above.
Here is information for Japan Airlines:
You should also contact the Japanese Consulate by phone, mail or email
to make sure you understand all the rules and regulations before making your reservations and preparing your cat for travel. If you have a Consulate or Embassy in your city, going in person, to speak to someone, is also a good idea.
I hope this information has been helpful, and please let me know if you need any additional info.
Good luck on your trip back to Japan with your kitty!