I think both of these options should be open to you. I’m an American woman with a Taiwanese and American son and I’m planning to spend the next year in Taiwan, too.
I was planning on getting a JFRV (Joining Family Resident Visa) to stay in Taiwan with my son, but I’m being told that I can’t do that because he’s a minor and can’t support me. (Last year, when I was planning to come, no one had a problem with this. :s ) But since you are the adult, and you have the Taiwnese passport, you should have no trouble getting a JFRV visa for your daughter. After you get this visa, you apply in Taiwan for her ARC.
Or, you can get a tourist visa for your daughter, and then apply for a resident visa for her, but this will mean paying for another $135 US visa, plus a trip back out of Taiwan again to change the visa, and then applying for the ARC.
So, you have two options, but take it from frustrated me–you’re lucky not to HAVE to shell out double expenses on this. You may have your reasons, but I can’t see any reason not to simply apply for a resident visa for your daughter before you leave, as this is what she will need in order to stay there with you for a year–and you CAN.
(I have to come as a tourist, do the pee-pee and poo-poo tests and paperwork for a job, then leave and get a resident visa sponsored by the boss, THEN, if I’m lucky, I can leave again and get the JFRV because I can show that I can support my child. And every time I do that, it’s another $135 bucks and trip off of the island. If I’m not lucky, I have to wait five years (I think) and apply for the PARK. See–? You’ve got it easy! )