While I don't foresee any problem with using any of the "local" addresses of the Department of Home Affairs, however, if you want it to be generic, why not address the letter as thru the Australian Embassy, for example:
Department of Home Affairs
Thru: Australian Embassy in The Philippines
Level 23 Tower 2, RCBC Plaza Tower 2
6819 Ayala Avenue, Makati City 1200
Philippines
I did that when I sent a letter of invitation for a visitor visa of my family.