Congratulations! Where will you be going in Asia? The requirements vary. You can get an idea of what you will need and quarantine laws by going to this site
http://www.pettravel.com/passportnew.cfm and selecting the country you will be visiting in the drop down menu. If you contact the embassy of the country you're going to they should be able to tell you exactly what you need so there are no mistakes. To return to the U.S. she will probably need a current health certificate.
As for flying in-cabin that depends on which airline you will be using. United and Lufthansa are letting me take my fur baby to Italy in-cabin, but many airlines will not. If you happen to be flying through England your furbaby cannot go in-cabin with you due to England's strict rules. Contact the airline and they will be able to let you know if your baby can fly in-cabin with you and what size/type of carrier he or she will need. If they say yes make sure you reserve your baby's ticket right away as there is usually a 2 pet limit in-cabin for airlines. Good luck!
Desiree & Eros