Customs and Excise
There are two separate government departments involved with bringing things to Australia. These are the Australian Customs and Border Protection Service and the Australian Quarantine and Inspection Service (Aquis)
Australian Customs and Border Protection Service intercepts illegal goods, such as drugs and weapons and they manage and determine excise duty on goods.
Here is a link to their guide for people coming to Australia: http://www.customs.gov.au/site/page.cfm?u=4258
For information about importing your car please refer to: http://www.customs.gov.au/site/page.cfm?u=4781
AQIS manages quarantine controls at our borders to minimise the risk of exotic pests and diseases entering the country.
AQIS also provides import and export inspection and certification to help retain Australia's highly favourable animal, plant and human health status and wide access to overseas export markets.
If you would like to bring your Cat/Dog with you to Australia you must get permission form the Aquis, prior to export. Please refer to the following link: http://www.daffa.gov.au/aqis/cat-dogs
If you have other pets please refer to: http://www.daffa.gov.au/aqis/cat-dogs/other
AQIS also determines products and items that cannot be brought into Australia from food to Animal products and even fishing and camping equipment: http://www.daffa.gov.au/aqis/travel/entering-australia/cant-take