Hi Susan
In the ESPL manual they provide a link to the Australian Charities and Not For Profit Commission. The ACNC website can be used to check the not-for-profit status of organisations.
Here is the link:
https://www.acnc.gov.au/ACNC/FindCharity/Simple_register_search/ACNC/OnlineProcessors/Online_register/Search_Simple.aspx?noleft=1&hkey=41c7c395-6b8a-4ca5-a9f8-a09b45e81a44
I have found all the owners of private schools in my area on this website.
Robert