Understanding that Australia doesn't have a Social Security ID (as the US does), might explain why passports play a similar role with respect to "proof of identity".
With passport and driving licence, you can do anything you want, but at least they are photo ID with some anti-forgery features.
The time to steal someone's identity is before they get their first driver's licence and passport!
Closest might be a Medicare Card which gives you access to free/discounted public health that can be used as part of identification. Usually children are on their parents card.
Drivers licence is also a primary identifier, and students can use their school student id.