Agree about the immigration records at the National Archives of Australia.
BDM records exist for each state and indexes are free online. However, there are privacy provisions and you will find states have limitations of when they will release records. In many it is 100 yrs for a birth etc. These rules will be displayed on the site of each BDM record.
Ryerson index is useful for deaths in NSW. Trove is the free newspaper site and many an obituary, death notice, funeral, birth notice wedding notice and description of wedding appeared in newspapers in Australia. You may also find descriptions of the voyage in the newspapers if by ship.
Regards
pH