Ancestry dont have many Irish records.. they recently added the BMD Index which, only covers civil record (i.e. after 1864), and collections of RC parish records (baptisms, marriages etc..) - but these cover only certain parishes in a few counties.
To search for records before the start of civil registration you need to know the denomination of your family, and where in Ireland they lived, so you can check what church records, if any, are available.
Many parish records are available on a free website at
www.irishgenealogy.ie, but this only covers a couple of counties (Dublin city, Co. Kerry, part of Co.Cork, and CofI records for Co. Carlow). Records for other counties are available of several pay-websites, but you would need to at least a rough location to check which, if any, suits your search.
see :
Introduction to Irish Records My Ancestor came from Ireland - where do I start? Shane