Yes, as you are registered for GST and are also an UberX partner you will need to pay GST on your earnings from UberEATS.
Through servicing thousands of users with ABN and GST registrations, a common situation we see is someone who starts operating as a food delivery driver and then later starts rideshare driving as well (e.g. through Uber, Ola, Didi, etc.). Rideshare drivers are required to have their ABN registered for GST no matter how much income they anticipate earning. In this situation, you are required to collect GST on all your food delivery income as well as your rideshare driving income that is earned through your ABN. It's at this point when you will need to prepare quarterly Business Activity Statements (BAS), to report your business income and expenses to the ATO and determine your overall GST position every period. You can find out more about BAS reporting here