No, that's not right.  In Australia, indigenous custom and law has survived and continues to exist alongside the received common law.

Each Indigenous nation has its own laws and customs. These are not written down but are passed on orally to each generation. In this way these customs and laws have been preserved to the present day and are increasingly recognised as a valid form of law despite being ignored and overridden for many years by successive colonial governments.

This form of law is mainly important in relation to family and community issues and land rights, but less so in relation to commercial matters.