I would apply for the Irish for your daughter but it still won’t change anything for how Taiwan would process her documents here as he mother is still from China. Be good if your wife gets her Australian citizenship then. Now will China still consider her a PRC citizen when it claims it does not recognize dual citizenship?
It would as gaining another citizenship after birth would cancel her chinese citizenship.
Unfortunately, this alone is not sufficient proof for Taiwan. Things changed a few years ago. i.e. @anon24369109 is correct.
When do you plan to all move? Before or after her AU passport comes through?
Original certification of non-establishment of Mainland household registration verified by the Straits Exchange Foundation could be ok.
My daughter doesn’t have household registration in mainland and I’m loathe to register her there.
Finding out if the document @tando mentioned is possible to acquire might be worth doing. It may not be asked for, but could be useful to avoid any similar problems for the rest of her life 
My family would likely follow after my wife gains citizenship… otherwise as I understand my wife could come earlier under a family permit TARC with no work rights.
don’t forget to get a certificate of loss of prc nationality at prc mission in australia. check if she should apply for it before or after she gets her australian citizenship. it may be much easier to get when she is doing naturalization, than to apply much later after completing the process and losing her valid prc document.
If you read FB groups and this forum you will find many people who were born in China even having foreign citizenship were not granted ARC/ TARC for Taiwan they had to use temporary visa’s and travel in and out.
to get her nwohr status by birth, you need to provide a nationality certificate of her lineal ancestor issued by roc government. as far as the roc government can authenticate the document and you can provide birth certificate of everyone in between and nobody got a hhr or passport from prc, it can be as old as her great grandfather’s or great great grandfather’s or older.
once someone got a prc hhr, decendants of the person lose the eligibility to apply for the nwohr by birth. they are a prc person if they provide their prc hhr certificate, and can get an roc hhr without a renunciation. or a foreigner if they provide a certificate of renunciation or a certificate of never having prc hhr, and need a renonciation for roc hhr. if they cannot provide any and their conection to prc is obvious to the roc government, they might be stucked to get any kind of residency in taiwan.
I see.
You said your wife is an Australian accountant working on citizenship, sorry I didn’t understand, is she Australian or not?
I think Chinese nationals can apply for regular ARC just fine if they meet the definitions of an overseas foreigner. This means if they were born in China, they need to have held a foreign citizenship and lived abroad for over 4 years. If they want to apply for APRC or Gold card then there’s more requirements around proving renunciation of Chinese nationality (they would want notarized documentation from the straits foundation for this), anything from China which isn’t verified by straits foundation can’t be used as proof. ROC doesn’t consider Chinese nationality law to be proof (which says you automatically renounce Chinese citizenship after picking up a foreign one).
Australian qualified accountant was in response to a question as to whether she was skilled (not in reference to nationality) …she is a chinese citizen.
Ok got it
Something to keep in mind is that anyone with Chinese nationality can’t acquire APRC (永久居留證). They are only allowed to acquire something called a “long term residency card” (長期居留證） which needs to be renewed every 5 years or so.
The National immigration agency also has their own policies for those born in China, and many of those policies were added ~2 years ago and not mentioned in the executive yuan law texts. For example showing proof of hukou cancellation if they want to apply for a gold card ARC.
Couldn’t that all work in their favour (my daughter and wife) as they could keep their Australian citizenship if they meet the 7 years of residence required to change their hhr to Taiwan. Or is that just on paper and the political realities and what documents are recognised make such an outcome moot?
If they’re able to do that then it could work out.
The regulations changed a lot for those born in China, HK and Macau over the last 3 years, who knows what’ll happen in 7 years. Some of the changes haven’t made it into law.
What you see in the law texts may be different from NIA’s interpretation is my personal experience.
I’m not very sure but years they stay as your (foreigner’s) dependents might not be counted for residency required to change their status. your wife might need to get her own residency as a professional, or they might need to be dependents of an roc national after you get a roc nationality by naturalization. you may want to read the laws and regulations carefully, or ask to nia.
a prc person may not get a residence permit as a dependent of a foreigner, just get a stay permit.
fyi
article 17 of Act Governing Relations between the People of the Taiwan Area and the Mainland Area
Your daughter does not have HHR in China though and as you stated you don’t wish for her to have that.
I know…i realised the inconsistancy when i wrote it. For her couldnt it be “establish”.
In all seriousness i think it would be better just to have her to be in Taiwan as an Australian.
Yup as she can enrol in international schools as a foreigner on an ARC.