Hi Patty,
Have you checked the excellent 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.
You could try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64). The Tithe Applotment Books (1823-38): Microfilm copies of the books for all of Ireland are available at the National Archives of Ireland (NAI) http://www.nationalarchives.ie/genealogy1/genealogy-records/tithe-applotment-books-and-the-primary-griffith-valuation/ or the Church of Latter Day Saints (LDS) https://familysearch.org/. Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at.
Civil registration records are available from the General Register Office (GRO). These start from 1864. You can access the website here: http://www.groireland.ie/research.htm . Valuations office in Dublin (http://www.valoff.ie) will have a record of the land registry from 1855 to modern times. This will assist in seeing what happened to any land the family may have owned (as it usually passed on to a relation).Church of Ireland parish registers for the period up to 1870 are public records. Registers are available for about one third of the parishes, however many were destroyed in the Public Records Office in Dublin in 1922. Most are still held by the local clergy, although some are in the National Archives of Ireland and others are in the Representative Church Body Library in Dublin. A list of all surviving registers is available in the National Archives. http://ireland.anglican.org/about/42 and http://www.nationalarchives.ie/.
You can check for information about the frequency of the name in the mid-19th century and any other variant spellings of the name here: http://www.irishtimes.com/ancestor/surname/
The Mallow Heritage Centre supports a database for Co Cork that is available for a fee at http://corknortheast.rootsireland.ie/
I wish you the best of luck with your search.
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Kind regards,
Genealogy Support
Ireland Reaching Out