I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Caution - The IFHF charges a 5 euro fee per rcd to view the details.
Note 1 - Without a KNOWN parish, the chance of an ancestor's rcds NOT being in this database is AT LEAST 35%.
Note 2 - Only 1/2 of Co. Cork's rcds are in this database.
Note 3 - The RC church kept control over most parish rcds from Tipperary (north). These are ONLY available thru the Tipperary Family History Research center at a substantial fee (regardless of outcome).
Note 4 - Each parish's rcds have their own quirks and limitations, too many to enumerate individually.
For Johanna Driscoll B 1863 +/- 4 yrs somewhere in Ireland with a father forenamed Edward, I found 0 B rcds. Are you sure of the father's forename.
Google the foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genform msg.