Robert Dore (1872); Mary Dore (1878) and Maurice Dore (1881) lived on a farm in Ballynoe and paid rent to a landlord named William Dore. They were there on the 1911 Irish Census. These are my father's uncles and aunt who stayed in Ireland after half of the family immigrated to the United States (Omaha, Nebraska). They would be the children of Robert Dore and Johanna Corbett.
There are 15 Dores in Limerick in the Irish phone book (www.118.ie/)
If none reply here you could do a mail out to the 15 as it's highly likely that some are descendants of your line; (it has worked for others).
Col