Public Record Office of Victoria: Passenger Records and Immigration
PROVs collection of passenger manifests
https://prov.vic.gov.au/explore-collection/explore-topic/passenger-records-and-immigration
National Library of Australia
The National Library of Australia has a detailed guide on using their collection to research family history
https://www.nla.gov.au/research-guides/family-history
National Archive of Australia’s Getting Started Guide
The National Archive also has a guide on how to search family history using their collection.
https://www.naa.gov.au/help-your-research/getting-started
Foreign Websites
Migration Museum
Some history on Australian convicts and searching from an English perspective.
Were your ancestors transported to Australia as convicts?
Find My Past UK
If you do find you have British history in the family, this website can help track back before migration to Australia. However this website is a paid one, but there is a free trial you could use if you feel it would be useful.
https://search.findmypast.co.uk/search-world-records/australia-convict-ships-1786-1849