Hi Murdoch,
Two thoughts...
1. A savings bond. Minimum term 10 years, small buy in, monthly contributions. They are 'tax paid' so nothing needs to be reported on Tax Returns (no nasty 'children's tax' * to worry about). After 10 years can cash out or keep going; I ran one for 12 years and then used it as most of a house deposit. I think you may be liable for tax if cashed out before the 10 year mark.
2. "Scholarship Funds" ASG - Australian Scholarship Fund is probably one of the better known ones. I think you need to start it before a child is a certain age and then you make regular contributions. If the child takes up post secondary study you make regular withdrawals from the fund. If the child does no further study you can cash out and receive back the amount you contributed but none of the earnings. My Sister and Brother In law set one up for each of their two kids. The oldest is in the final year of uni; they have set the withdrawals at the same rate as Ausstudy; kid lives at home, gets the money and can concentrate on studying. She uses it for transport, phone, textbooks etc. Second child is year 12 this year so not sure of the plans there but they will offer her the same deal.
No idea of the tax treatment with option 2
I don't think a child can buy shares in their own name; there would need to be some sort of trustee arrangement.
* Children's tax applies to 'unearned' income directly in a child's name. This generally covers dividends, interest and trust distributions. It was established to prevent tax minimisation by placing an adult's assets in a child's name or by making the majority of distributions from a trust to a child that has no other source of income. The rates are:
$0 to $416 rate is nil
$417 to $1,317 rate is 66%
over $1,317 rate is 45%
But, with current interest rates you would need more than $10,000 in the bank to be triggering the children's tax. Well before hitting that mark I would be doing something else with the money.
In terms of opening a bank account you would need to check with the various banks as to their requirements in terms of age etc. Many kid's accounts have 'bonus saver' type features to encourage a regular saving habit.
Another option to consider (if you have a mortgage) - stick their money in your offset and track with a spreadsheet. This will give you a guaranteed tax free return equivalent to your loan interest rate. Again, when you accumulated a lump look at your options.