Ancestry.com is a subscription site with worldwide content. The library edition is available to use for no charge within the building of the State Library of Western Australia and at most public libraries in Western Australia. Top content includes Australian electoral rolls, Australian passenger lists, convict material, UK census 1841-1901, UK birth, marriage and death indexes 1837-2005, UK National Probate Calendar 1861-1941, British phone books 1880-1984, London parish records, New Zealand electoral rolls 1853-1981, United States census, Canadian census and much more. The commercial (non library) version at www.ancestry.com includes publicly submitted material such as family trees and photographs.
http://catalogue.slwa.wa.gov.au/record=e1000219~S2
The State Records Authority of New South Wales website has many useful online indexes including passenger lists, convicts, divorces, probate, naturalisation and more.
http://www.records.nsw.gov.au