The following moderators provide local knowledge and expertise for Cockroaches (Blattodea, several families):
CarbonAI | Curiosity | Aussiegall
A good reference for Cockroaches is the book “A Guide to the Cockroaches of Australia” by David Rentz. https://www.publish.csiro.au/book/6710/
This webpage by the CSIRO is also useful:
http://anic.ento.csiro.au/insectfamilies/order_overview.aspx?OrderID=42509&PageID=overview
No species currently belong to this list.