Where is home? If it's the USA, Stray Dog just found this for me:
US Customs Q&A site
(I know rabbits aren't rodents, but some Customs inspector might not understand that.)
You still have to go through the export process for Taiwan, including the vet exam and the paperwork from the quarantine office.
EVA allows them in-cabin in an underseat container. EVA's website is very clear about this. The 5kg weight limit for in-cabin probably applies, so if your cage plus rabbit weighs more, it'll go in the hold (or if you're traveling with someone else, you could probably each take one in separate carryon containers).
I'm feeling rather pro-EVA right now because they are the only airline I have contacted which was not a royal pain in the ass about pets and specifically rabbits. Three other airlines ran me around in circles for a week or two each before eventually letting me know that they either don't take pets or refuse to accept rabbits specifically. EVA, on the other paw, has been a ray of sunshine, clearly stating on their website that they think rabbits are wonderful little creatures who deserve to be allowed to travel in the cabin in comfort and with in-flight beverage service. I think everyone should fly EVA from now on.
EVA Air pet FAQ