From the Department of Transport Website:
When can vehicles be sold without a Safety Certificate?
The only time vehicles do not require a certificate to be sold is when they are unregistered or when they are traded to or between licensed motor dealers. Vehicles can still be sold for parts or restoration, but they must be de-registered before being offered for sale.
How long are Safety Certificates current for?
Make sure certificates are current. For dealers, certificates must have been issued in the previous three months or 1000 kilometres prior to sale, whichever comes first.
For private sellers Safety Certificates must have been issued in the previous two months or 2000 kilometres prior to sale, whichever comes first.
Selling a vehicle?
If you are selling a registered vehicle, you will need to obtain and display a Safety Certificate from the time you offer the vehicle for sale.
Once you have a Certificate, which identifies the Approved Inspection Station which issued it, you must display it on the vehicle from the time the vehicle is offered for sale. Click here for a seller's checklist.
If you fail to display a Safety Certificate on the vehicle from the time of sale you will receive an on-the-spot fine of $375.
Displaying Safety Certificates
Safety Certificates must be displayed in a very obvious place.
FOR EXAMPLE...
Motorbike - front forks or guard
Car - windscreen or window
Trailer - draw-bar