Yes you can. There are many ways to do this, both online and offline. I resisted the need to sign up for a paid subscription site for many months before I finally gave in to temptation and signed up to Ancestry.com. To be fair my research went ahead in leaps and bounds after I signed up to Ancestry so it is worth checking your local library to see if they offer free access to Ancestry and FindMyPast.
Apart from finding free access to the paid subscription sites, it's always worth checking with your State Library. Most have family history collections as does the National Library. They also have a range of family history guidelines publications on the type of family history records they hold as well as advice on how to access them. Some are on line, for example the State Library of Victoria's wonderful picture collection and the Ryerson Index which has death notices and obituaries from Australian newspapers dating back to 1831.
While the State Libraries have private sector records in their collections, your State Record Office is the place to go for government records dating back to the early days of the colony and are slowly being digitised. It's well worth searching the online catalogues to find likely record sets which are relevant to your research and visiting their office in person to undertake offline research. The rewards are waiting there for anyone with the patience and determination to succeed.
Apart from paid subscriptions to the major online databases, there are a many free sites which should be part of your online family history tool chest including:
Trove - the National Library of Australia's online database of newspapers. This free resource is the taxpayers' gift to family historians. Without it I would never have discovered so much information about all branches of my family - www.trove.nla.gov.au/
National Archives of Australia - www.naa.gov.au/
The State Library of New South Wales, part of which is known as The Mitchell Library - http://www.sl.nsw.gov.au/
State Library of Victoria - www.slv.vic.gov.au/
Victorian Public Record Office - https://prov.vic.gov.au/
Victorian Births Deaths and Marriages - https://online.justice.vic.gov.au/bdm/indexsearch.doj
Australian War Memorial - www.awm.gov.au
I will be reviewing these and other record repositories in detail in the coming months.
Your Family Genealogist
Picture : with thanks to Pixabay