From the 1st of July 2015, the office responsible for issuing Apostilles on Australian Public documents is the Australian Passport Office located on the 17th floor, 150 Charlotte Street, Brisbane QLD 4000.
Staff at Australian High Commissions and Consulates overseas with access to the Australian Consular Information System (with the exception of Honorary Consulates), will be able to issue Apostilles on Australian Public documents or those certified by Australian notaries public.
For further information, please consult the Smartraveller site: http://www.smartraveller.gov.au/authen.html