It's a natural human curiosity to want to know where you came from. Not knowing where to start can often be the daunting part but once you make the initial queries and discover some interesting facts it often leads to further lines of enquiry. Before you know it you have gathered a wealth of information you would never have known had you not taken that first step. Researching your family history is a very rewarding yet time consuming project but I'm sure you'll agree, it's well worth the effort.
If you just starting out and not sure where to look, I have put together a list of links to help you with your search. Good luck!
National Archives of Australia. http://www.naa.gov.au/collection/fact-sheets/fs170.aspx
Estonian Archives in Australia. http://archives.eesti.org.au/
From Estonia to Thirlmere.
Australian Department of Immigration. Immigration history 1945-1955.
Australian displaced persons down under.
Bathurst migrant centre Australia.
Bonegilla migrant centre Australia. http://www.bonegilla.org.au/
Uranquinty migrant centre Australia.
National library of Australia http://trove.nla.gov.au/
Australia's migrant heritage. http://www.migrationheritage.nsw.gov.au/belongings-home/about-belongings/australias-migration-history/
State records of NSW. www.records.nsw.gov.au
If you require help researching you family in Estonia, the Estonian Biographical Centre accept orders to complete the research for you. More information can be found at: http://www.isik.ee/english/
Alternatively, you can search through the documents yourself at the Estonian Archives. http://ais.ra.ee/