The standard talking point coming out of the ABS is this scenario:
The Census form is the only reliable source of information on whether an individual identifies as being of Aboriginal or Torres Strait Islander. So, after the census, if the census name, DOB, and address records are matched against new death records a better picture of indigenous Australian life expectancy can be made. That information is useful when planning programs to improve indeigenous life expectancy.
Neither birth nor death records carry this indigenous origin information. However, it strikes me that this can be achieved a number of ways without keeping the actual name, DOB or address. Hashes of the components (normalised or perhaps several allowing for variant spelling) can just as easily be compared and the sensitive data is never retained.
There are currently legislated protections forbidding the use of this data for any other purpose including law enforcement, courts, or taxation. However, these can easily be remove by an Act of parliament (and are probably already subverted for intelligence agencies). I do not trust future parliaments.