Although convict settlement in Australia is infamous, more people settled as free settlers, and the number of these swelled after gold was discovered in the 1850's, as well as the large numbers that arrived in the 20th century on the assisted passage scheme.
Aside from the general Passenger Lists there are other sources specific to Australia that may be of relevance, only some of which are available online.
The UK National Archives has a number of important records for newly arrived Australian migrants. The Colonial Office papers relating to the governance of New South Wales during the 19th century all contain names of immigrants. They can be found in series CO 201 (this & CO 208 are the only ones for which Microfilm copies are available at the National Library of Australia, the State Library of Victoria, and the State Library of New South Wales, Mitchell Library, Australia), CO 202, CO 360 and CO 369. The archives of the New Zealand Company are available at CO 208.
The New Zealand Government has a very good History of Immigration online & the Tasmanian Archives have a very good website, which includes a searchable names index.
The Australian government took various censuses of convicts in New South Wales and Tasmania at various times from 1788 onwards. Although primarily concerned with recording convicts, they would also include those who were not transported. It is possible to find other genealogical data, such as age and occupation of these individuals in these censuses, found in HO 10.
The Society of Genealogists also has a good number of records, including some useful reference material, biographical dictionaries, early directories, lists of settlers, and inscriptions. Microfiche indexes to the births, deaths and marriages in Australia (except Tasmania) and New Zealand from the earliest times up to about 1900 are available in the Lower Library, together with lists of the wills proved in Victoria to 1899 and in New South Wales to 1980. Births, marriages and deaths in Tasmania 1806-99 are on CD-ROM in the Lower Library. There is a copy of the 1828 Census of New South Wales and of the 1882 Return of Freeholders in New Zealand.
The National Archives of Australia has only a limited amount of information, apart from the 20th century, as matters of immigration were not federal policy until 1901, . Prior to that each of the 6 states would control immigration and their archives contain a variety of information. However it does have a section of its website dedicated to Family Historians with much useful information and is well worth a visit.
It's also worth giving the IGI (International Genealogical Index) at FamilySearch a try, as they have records for both Australia and New Zealand.
The website Adelaide Proformat has a list of all the musters & census's taken between 1788 & 1901.
More links for genealogy sites for all of Australia can be found at Genealogy Links, Cyndi's List (AUS)& Cyndi's List (NZ).
Ancestry.com has the following records as searchable indexes (subscription necessary to view records):
New South Wales and Tasmania, Australia Convict Musters, 1806-1849
New South Wales and Tasmania, Australia, Convict Pardons and Tickets of Leave, 1834-1859
New South Wales and Tasmania, Australia, Settler and Convict Lists, 1787-1834
New South Wales, Australia 1828 - 1842: Bounty Immigrants List - Free Index
New South Wales, Australia Convict Ship Muster Rolls and Related Records, 1790-1849
New South Wales, Australia, Assisted Immigrant Passenger Lists, 1828-1896
New South Wales, Australia, Certificates of Naturalization, 1849-1903
New South Wales, Australia, Unassisted Immigrant Passenger Lists, 1826-1922
New South Wales Free Settlers 1826 - 1922
Australian Convict Transportation Registers – Other Fleets & Ships, 1791-1868
Australian Convict Transportation Registers – First Fleet, 1787-1788 - Free Index
Australian Convict Transportation Registers – Second Fleet, 1789-1790
Australian Convict Transportation Registers – Third Fleet, 1791
Historic Electoral Rolls 1842 - 1864 (Coming soon)
1828 & 1848 Census's (Coming soon)
The 20th Century
During the 20th century more than seven million people made Australia home. The National Archives project Making Australia Home is progressively making migration records available online.
The project involves listing individual migration records collections on an online database and making digital copies of these migration records available to view online. Migration records in the National Archives cover many millions of people who made the journey to Australia, including postwar displaced persons, those who travelled on assisted passage schemes and new arrivals who stayed in migrant accommodation centres like Bonegilla.
The records typically include personal details, such as name, nationality, date and place of birth and information about family members. In some cases there are photographs on the files.
The first step to finding out whether the National Archives holds migration records about you or your family is easy.
NameSearch, part of the RecordSearch database, lets you search specifically for migration records.
Simply enter the family surname and select 'Immigration and naturalisation records' using the drop-down list. Make sure you try variations of the name if you don't find records on your first attempt.
Many migration records have already been digitised as part of this ongoing work. They are identified in RecordSearch with a 'View digital copy' icon.
As well as these proactive digitisation projects, you are able to purchase online copies of records. When you have found a record you want in RecordSearch, simply click on 'Request copy' to order an online copy. The record will be placed onto RecordSearch and you will be notified by email about how to find and view the images.
The National Archives in Australia also have a good set of online Fact Sheets for those wishing to research their Family Histories on how to use the archives, what's available and where to look beyond.