.org.au domains can be registered only by non-profit organisations. As proof of this, you will need to provide either your Australian Incorporated Associations Association number (e.g., Y12345 or A12345) or your ABN.
Sole traders etc. are not eligible for an .org.au domain name.
The legislation for this was recently loosened, so you do not have to be a registered organisation to get an org.au domain.
You can register an org.au domain as a non-registered organisation by putting 0000 in the ACN field.