How to buy shares for my child in their name, page-18

I am not 1000% sure how each broker does it, but setup the account a "trust"

how the holding should look.
Your Name
<A/C Kids Name>

https://www.commsec.com.au/support/frequently-asked-questions/404.html
Can I buy shares for a minor?
CommSec cannot trade on behalf of a minor. You can however open an account in the name of an adult who will act as trustee until the minor turns 18. Once the minor has turned 18, the shares can be transferred into an account in their name.
To create an account in trust for a minor:Click on the 'Join Now' icon on the CommSec homepage, select the product you would like to apply for and click 'Get Started'.Under 'Which account would you like to apply for', select 'Trust' and 'Minor' for the trust type


Taxation - who controls the shares - you do (or your partner) - you pay tax/CGT, however, once kids turn 18, shares transfer to them, they start to pay tax, no CGT on transfer as they always "owned" them.