If you are talking Compulsory Third Party as included in the rego that covers people who the CTP driver hits.
Not ALL cars on the road are registered. They legally should be but they are not. Qld is removing rego labels soon so have fun checking if the car is registered.
Most comprehensive insurance that you (as a car owner) take out to protect your car specifically excludes taking fee paying passengers. So no coverage there.
Just FYI an average 6cyl car in Qld is about $800 to rego (including CTP), a taxi is $7000 including CTP. I wonder why? More risk of accidents as more time on road...just like Uber.
DTMR or Queensland Transport have volumes of legislation regulating safety, insurance, drivers, operators, passengers and booking companies.
They all expressly forbid outfits like Uber. Uber are not the first to try the legislation either. The other have closed or come within the legislation.
Suggest you read the Queensland Act - Transport Operations - (Passenger Transport) Act 1994
Other states (and countries) have similar act to protect the public