This tells you about the
requirements for studying in NZ and may throw up a couple of obstacles, one being that, with her not being under your PR umbrella, she would be liable for international fees if she studies and I understand they can be quite hefty. Another problem is that it says she needs to show that she is going to leave NZ as soon as her study period is finished, also that she needs to show proof of sufficient funds to support herself while she is there studying. It would take a lot of looking into to get it right.
Can I ask which visa she holds at the moment? I was about to suggest she try a Working Holiday Visa for 30 year olds and under, but there isn't such a scheme available for SA, which surprises me.
Because of the circumstances, I wonder if it would be worth going to the head of the well and asking advice from INZ themselves. Does your daughter have any close family back in SA? If not it would be another string to your bow when you try to keep her with you. I wouldn't think SA would be the sort of place for a young woman to be on her own without the protection of close family members.