I can’t really make a lot of sense from the responses to your post, but if your girlfriend is having the baby here, I don’t think you’ll have any rights at all if you’re not married. Maybe the Taiwanese authorities now recognize the birth father of a child born out of wedlock, but it must be a pretty recent thing if they do, I think.
Do they allow the father’s name to be put on the birth certificate if the child is born out of wedlock? I don’t know, but I don’t THINK they do. In which case, it will be rather difficult to register its birth in Oz if you’re not in the picture on the birth document, won’t it?
I think you need to get your girlfriend to talk to the authorities here about it rather than relying on the unsubstantiated word of a bunch of people who have little idea about what they’re talking about most of the time. This is your child’s future you’re talking about, not what’s the best kind of motorbike for Taiwan’s mountains or the latest promotion at Costco.