GST (Goods and Services Tax) is a unified Australian 10% tax on most goods sold in and to that country. GST is a nationwide tax, no additional state taxes apply.
You are required to register for and charge this tax if your annual turnover in Australia has exceeded the threshold of 70 000 AUD.
If your annual turnover in Australia has exceeded 75k AUD you will need to register for GST in the Australian Taxation Office (ATO).
To be able to do that you will also need an Australian Business Number (ABN).
There are certain products and groups of products which are GST free (you will not be required to charge GST on these sales even if you have exceeded the annual 75k AUD threshold).
Mostly these are medical, health and educational products.
For a full list of the GST free products please see here.