For GST purposes, if you haven’t done a logbook the ATO allows you to make a reasonable estimate of your Uber percentage based on records such as odometer readings or service records.
Note that there are different rules for income tax. For your end-of-year tax return, if you haven’t kept a formal logbook, you’ll be limited to a maximum claim of 5,000kms at 72 cents per km, giving a deduction of $3,600. For infrequent drivers this may be plenty, but if you drive greater hours for Uber a logbook may be well worth the trouble. Read more about keeping a logbook here.