You have finally taken the leap and you are going to be self-employed. The most basic business structure you can trade as is a Sole Trader. Being a Sole Trader, you are the business. All you really need to get started is:
 

To apply for an ABN
Registering for GST is only compulsory if your income (not profit) is above $75k annually
If you would like to have a Business Name, you will need to register this business name with the ASIC.

One of the biggest challenges for new Sole Trader is putting money aside to pay their tax. As a rule of thumb, I advise most clients to put aside 30% of what they earn for tax, i.e. savings. You can use these extra savings for super contributions, as you no longer have an employer paying these for you.

Sole Traders no longer are covered by workers compensation insurance, I would recommend getting some sort of sickness and accident insurance which is similar.

These are some challenges before you start dealing with customers...