Household bills are gas and or electric, which should be much cheaper, unless of course you run the a/c all day long. You'll have water/sewerage rates, plus council rates. You don't need tv licences in Aus.
In NSW you have your yearly car registration. Over three years old, your vehicle must have a pink slip (test for road worthiness) and a green slip (compusory third party ins, which only covers your passengers, and any other persons injured in an accident, when you, or the person driving your car is at fault). You still need car insurance to cover you for any damage to vehicles or property etc. You can choose either third party, or fully comprehensive.
Other states have their own laws.