I have heard a lot of different views on what the legal requirements are for transporting dogs in cars. Australian states all have slightly different rules. For New South Wales according the the RTA:
"The Prevention of Cruelty to Animals Act states that a person must not carry or convey a dog (other than a dog being used to work livestock), on the open back of a moving vehicle on a public street unless the dog is restrained or enclosed in such a way as to prevent the dog falling from the vehicle.
Please see below link to view this Act (see rule 7):
Dogs should not ride unrestrained in either the front or back seats of any vehicle but this is not specifically stated in legislation. The police may fine you however if they deem that you do not have proper control of the vehicle due to the animal interfering with your control. Specially designed animal boxes and harnesses are available and should be used. A pet harness can be attached to the vehicle's seat belt allowing the dog to sit or lie on the seat.
It is stated in legislation that a driver must not drive with a person or animal in the driver's lap. This is Road Rule 297 (1A) Drive motor vehicle with person or animal in lap
To view the complete road rule please click on the below link to find Road Rule 297.
So, I think you can take your dog in a car back seat un restrained, but if you want to be super safe buy a harness and a harness set belt connector. We have seat belt clips now in stock. Mention this blog and I will give you one free with your Back Seat Protector purchase!