I don't know if this is the right SE for this question, and standard IANAL disclaimer here (followed by I Am Not An Accountant), however, I am Australian and do have my own ABN (so that may help?)
It depends entirely on your business structure. If you are directly engaged in providing a product or service to someone then yes, you are required to have an ABN and register for GST.
The Australian Business Register website covers the basics of what the requirements are for an ABN.
The plus side, though, is that applying for one is free, fairly easy and relatively quick (well, as quick and easy as any dealings with the Australian government are).
Something to also bear in mind is that as part of your tax return, you do need to specify if part of your income stems from royalties associated with books, music etc.
The benefits of using a platform like Amazon or any of the other self-publishing (or even traditional publishing) organisations is that you, directly, do not require an ABN.
However, keep in mind that if you do decide to get an ABN, and set yourself as a sole trader (in a similar fashion to say, a photographer), you will be able to claim expenses related to your business of writing. Things like equipment, a percentage of power and data etc.
But the biggest advice (and really, the only) is to talk to an accountant. A good accountant will help you set things up correctly, and so that it has a minimal impact, financially, on you.