Have the vehicle inspected at an independent inspection station. Pebcos Automotive in Hamilton Hill (08 9434 1361) is recommended. The cost is approximately $75.
Take the inspection report along to a Licensing WA office along with your existing registration document, identification documents and a utility bill showing your name and WA address.
Fill in the required forms and they will give you a new set of plates. There is no requirement for 3rd party insurance - it is included in the registration fee.