Adelaide (the capital of South Australia) is about 500 miles from where I live.
The registry would be kept at one of their central archives and you would only be allowed to check a record from the period of question if it was your own record or that of a dependent.
Do you have an account on ancestry.com?
It would seem that the courthouse people could be asked if, during the relevant time frame, these kinds of documents referenced a book with all those numbers? No personal details, just about the type of documents kept then.
Oh good grief. You should have seen me scouring court house records in every county within 100 miles. I was aking for birth records, marriage records, death records, census records and criminal records. The clerks were more than happy to pile those books up in front of me and walk away. I guess America is (for now) freerer than any country.