Hi Colleen
Thank you for your query. Firstly did you acquire the information that you have from personal family documents or public records? Include information concerning which sources you may have already used so others may further your search.
Have you checked the immigration records in Australia? Generally, more information was given at the port of arrival rather than the port of departure. The University of Woolongong has produced, on microfiche, a complete index and transcript of all information concerning immigrants of Irish origin recorded on ships' passenger lists between 1848 and 1867. These are useful for finding out an exact place of origin as well as parents' names. The Public Record Office of Victoria has good online databases of settlers at www.prov.vic.gov.au Otherwise, other records may be found in the Colonial Office Papers of the UK National Archives, class reference CO 201. This class contains a wide variety of records, including petitions for assisted passages, emigrants' lists, records of emigrants on board ship, petitions from settlers for financial assistance and much more.
http://www.nationalarchives.gov.uk/records/looking-for-person/
You could try checking the land records called the Tithe Applotment Books (1823-38) http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp or the later Griffith's Valuation (1848-64) http://www.askaboutireland.ie/griffith-valuation/ or the Church of Latter Day Saints (LDS) https://familysearch.org/
The Tithe Applotment List might be of use to you, or at least interesting for you. These lists constitute the only nationwide survey for the period, and are valuable because the heaviest burden of the tithes to the Established Church, the Church of Ireland, fell on the poorest, for whom few other records survive.
Colleen here are some other websites that may be of help to you:
http://www.irishtimes.com/ancestor/browse/
http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
http://www.nli.ie/en/family-history-introduction.aspx
http://ifhf.rootsireland.ie/?gclid=CKLT_Pa4wrUCFYUf4Qod4EoAGg
Kind regards,
Genealogy Support