Congratulations @Jamesw, both on the arrival of your daughter and taking some proactive steps towards giving her a great head start.

Cooperative Bank Youth accounts are I think currently the best available (did require me becoming a member with a zero balance savings acc.) which earn 3% interest on the first $4000 deposited, and 0.75% on anything over $4000. I think it's the best child account around at the moment and it may suit your needs, at least initially. (Youth account is zero fees for anything and is up to the age of 12!)

If you go down the shares route I'd advise against buying in your child's name (e.g. getting them a CSN etc) as it'll just cause grief later if you want to sell quickly, or at all. Nothing in NZ seems well setup for children as the admin is always done under the guise of the guardian's account. A good example is Westpac online term deposit setup, works... but defaults to guardian's tax rate, requiring a phone call and several days to fix.

You didn't mention it, so apologies if you know this already, but the government's BestStart plan is a must have, everyone gets it for the first year and then there's an eligibility requirement after that; https://www.ird.govt.nz/topics/worki...out-best-start