Many units have published unit histories, which can usually be located thorough local or state public libraries or the Research Centre at the Australian War Memorial (AWM): Australian War Memorial Research Centre.
The AWM's online book catalogue contains the title and publication details of numerous unit histories: Search AWM's online book catalogue.
The AWM holds War Diaries maintained by the units during hostilities which can be a useful source of information. These can be accessed at the AWM. War Diaries are a concise, accurate, day-to-day operational account of the unit, but can vary considerably in quality and diaries unfortunately do not exist for every unit that served.
The AWM has an ongoing project to scan the diaries and publish them online so a first check should be made of the web site: Australian Army War Diaries.
A microfilm copy of the diaries can be viewed in the reading room of the AWM Research Centre. If you are unable to view a copy of the unit diaries yourself, you may wish to engage a research agent to undertake research on your behalf.
The AWM web site also contains brief histories of Australian First and Second War units: Australian Military Units.
A further source of information is the official history of the relevant conflict, such as C. E. W. Bean's The official history of Australia in the war of 1914–1918 (Sydney: Angus and Robertson, 1937). This is available online through the AWM: Official History of Australia in the War of 1914-1918.