Overseas vehicles are usually built to different specifications to those required for the Australian market. Do not assume that a vehicle that seems to be identical to a model already available in Australia meets the required Australian Design Rules (ADRs). Generally, only vehicles that have been built specifically for the Australian market comply with all of the required ADRs.
Vehicles for use on public roads in Australia are usually required to be Right Hand Drive (RHD). Contact your local State or Territory Registration Authority for information on acceptance of Left Hand Drive (LHD) vehicles.
Insurance cover, other than compulsory third party, may be difficult to obtain for used imported vehicles.
http://www.infrastructure.gov.au ... Considerations.aspx
Before your vehicle arrives at port, you must already have an import approval or you may face prosecution and significant storage costs. Additionally, you may be charged by Customs a duty fee of $12,000 AUD. Any vehicle that has arrival and has been rejected due to rust, corrosion or contamination may either need to be exported out of Australia or destroyed. LeftHandDrive vehicles usually must be converted which is expensive.
Below is from your provided link. Having not gone through the whole page and not yet found whether it applies to family cars, but it seems, in certain conditions, that left-hand driving cars can be on the road.
Left Hand Drive Vehicles
Light (not over 4.5 tonnes GVM) Left Hand Drive vehicles are not required to display a "Caution Left Hand Drive Vehicle" sign. Left hand drive vehicles over 4.5 tonnes are required to display a "Left Hand Drive" sign on the rear of the vehicle in words at least 75mm high in a colour that contrasts with the background to the words.