If you choose to begin as an UberEats partner, you will need to register for an ABN. You will not be required to register for GST purposes unless you are earning $75,000 from this activity annually. If you were to start rideshare driving, your ABN will be required to be registered for GST, and you would need to collect GST on all your UberEats deliveries and Uber rideshare trips.
It's at this point when you will need to prepare quarterly Business Activity Statements (BAS), which are used for reporting and paying a number of tax obligations, including GST and pay as you go (PAYG) installments.