Yes! A relatively cheap and straightforward way for foreigners and non ABN holders to own Australian domains is to simply apply for an Australian Trade Mark at the Government’s website, IP Australia. They are then eligible under Schedule C, Section 1F and Section 2A of the “Domain Name Eligibility” policy to buy Australian domains.

 

Below is the text from the mentioned Policy sections. The relevant eligibility clauses are coloured green.

ELIGIBILITY AND ALLOCATION RULES FOR COM.AU

 

The com.au 2LD is for commercial purposes.

 

The following rules are to be read in conjunction with the Eligibility and Allocation Rules for All Open 2LDs, contained in Schedule A of this document.

 

1. To be eligible for a domain name in the com.au 2LD, registrants must be:
a) an Australian registered company; or
b) trading under a registered business name in any Australian State or Territory; or
c) an Australian partnership or sole trader; or
d) a foreign company licensed to trade in Australia; or
e) an owner of an Australian Registered Trade Mark (‘TM’); or
f) an applicant for an Australian Registered TM; or
g) an association incorporated in any Australian State or Territory; or
h) an Australian commercial statutory body.

 

2. Domain names in the com.au 2LD must be:
a) an exact match, abbreviation or acronym of registrant’s name or TM; or
b) otherwise closely and substantially connected to the registrant.

 

Here is the complete Policy:
Domain Name Eligibility and Allocation Policy Rules for the Open 2LDs.

 

To apply to register an Australian Trade Mark:
1. Apply online at IP Australia; or
2. Contact Cooper Mills an Australian Law Firm. (recommended)

 

See also:
1. Registration of AU Domains by Foreigners, by Cooper Mills Lawyers
2. Cooper Mills Trade Mark Infographic

 

I am not a lawyer. This is not legal advice.