Hi there,
Could you please post yoiur message here (Londonderry): http://www.irelandxo.com/group/templemore-derry
There are three Roman Catholic dioceses for Londerry/Derry city:
Derry City: St. Columb's (Derry) - Baptismal records start from 1823, marriage records from 1823
Derry City: St. Eugene's Cathedral (Derry) - Baptismal and marriage records from 1873
Derry City: Waterside (Derry) - Baptismal and marriage records from 1864.
If you have any difficulty, you could try contacting the parish priest for the area.
There are two websites about County tyrone you might find interesting: http://freepages.genealogy.rootsweb.ancestry.com/~tyrone/ and http://cotyroneireland.com/
You should look at the land records called the Tithe Applotment Books (1823-38). The family may be listed here.
Also worth checking are the Spinning Wheel Premium Lists (1796). There are over 7,000 names listed for County Tyrone. This can be viewed here: www.failteromhat.com
You should check for more information about the ship and it's cargo/contents/names in Australia. Generally, information was given at the port of arrival rather than the port of departure. Do you have any idea about the circumstances for their move to Australia? Perhaps, you might be able to find a lead for this, when you find out about the ship.
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)