Your girlfriend is happy with staying in NZ??? Christ, you won the lottery buddy, just take it and run! Do NOT move to Taiwan. I wish I had the choice to stay in America but my girlfriend just can't bear the thought of being away from her parents... Ugh.
There is absolutely no reason for your child to learn Taiwanese. If you really want her to learn Taiwanese, you'll need a tutor. Schools don't teach it, really, and less and less kids know it. In fact, my girlfriend's generation (she's 25) doesn't even know much beyond "Hello", "How are you?" and "I love you".
I also had this idea before I moved to Taiwan. I had the same train of thought. I wanted my kids to learn Chinese and Taiwanese. Then I realized Taiwanese is useless and they'll learn Chinese regardless of where they grow up. The school system in Taiwan is a tyrannical system, filled with loathsome abusive teachers, copious national tests, and practically requires children to go to cram schools to stay competitive.
I'm not just warning you, I'm telling you, PLEASE don't move to Taiwan. Taiwan is a country great in small doses, but the children here grow up soulless products of a machine that grinds out spoiled, abused, monsters. Your children will also be subject to intense racism in their early years in Taiwan, as other kids struggle to comprehend why she looks different. She will be called names, she will be treated unfairly by her teachers, she will be hated by her peers.
Furthermore, if you do move to Taiwan, it's likely the in-laws will be paying lots of unexpected visits and requiring you to visit them, if not move in with them entirely. No matter how independent your wife is, few Taiwanese women can ignore their mothers wishes when confronted with them so directly.
You have a good career in NZ. Keep it that way. If things don't work out in Taipei, and they won't, there is no guarantee that this career will be waiting for you when you come back. You're taking an unnecessary risk. I'd say, save money up for annual visits during Chinese New Year and during her summer vacations at school. She can visit and stay with the grandparents then for a few weeks and that'll be enough. But please, please, please do NOT subject your child to that torture. I wouldn't wish it on any child, and a half-Asian child will face inconceivable sums of discrimination and hardship.
One other thing. I love Taiwan. Maybe it doesn't seem that way, but I do. It's just a very complex relationship we foreigners have with Taiwan, you see... It's truly love-hate, give and take. Some stuff about Taiwan I totally adore, but other things I loathe. Where you stand depends on where you sit, really. Maybe Taiwan will seem enjoyable to you if you have a good job here (though I don't see how you will since the one thing Taiwanese value more than their parents is a good degree), but you're still torturing your child, and the sad thing is your child won't even know that there is something better out there by the time she is old enough to be asked "Do you like it here?"
You said in your message that you found Taiwanese people to be very friendly. That's great that you've had that experience, I think it's how we all feel before we live here. Taiwanese are very polite to foreign tourists, but as you stay you'll realize that the system itself is racist, Taiwanese are not very polite (not even to each other), and as the make up fades, everything in Taiwan seems to lose its rich flavors and colors.
I wish that my experience here was always the same as my first week in Tapei. Ignorance is bliss. That being said, I very well may spend most of my life here, and I won't be that unhappy, but for a man in your situation, please don't make the same mistake. For your children, if not for yourself, stay in New Zealand if you have the chance.