The National Library of Australia's Digitised newspapers and more is the single best resource for finding Australian news. Coverage varies, so it is important to check available dates.
Trove includes almost every major Australian newspaper (only limited content for The Age), as well as many lesser titles. You can limit your search by title, state or date range.
Some of these resources are available only to University of Melbourne staff and students. You will need to enter your email username and password.