Hi there,
It looks as though Ballyduff parish is in the Roman Catholic diocese of Killiny. The church records for here date from 1828 for baptismal records and 1829 for marriage records. You can find these at the National Library of Ireland, Pos. 4275 to 1864; remainder 4276. If you have any difficulty, you could try writing to the parish priest for more assistance. You can also find these (fee paying) at the Killarney Genealogical Centre. It is possible that some of the children were born in neighbouring parishes.
Civil registration records are available from the General Register Office (GRO). These start from 1864 however. You can access the website here: http://www.groireland.ie/research.htm
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64). 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. 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).
Have you checked the immigration records in Australia? You have the name of the ship and a date, so this will help a lot. 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 useul 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, peitions from settlers for financial assistance and much more.
There is a book you might find useful by Michael O'Connor called 'A Guide to Tracing your Kerry Ancestors', 1994.
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,
Sinead Cooney
Genealogist (Ireland XO)