I research 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.
Note 1 - Without a KNOWN county, 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).
For Marg(aret) Doolan B 1833 +/- 1 yr in Co. Limerick with a father forenamed Laurence, I found 0 rcds.
For Mary Doolan B 1831 ditto, I found ditto.
For Laurence Doolan M 1828 +/- 2 yrs somewhere in Ireland, I found 0 rcds.
For Marg(aret) Digan M ditto, ditto.
Note - King's (Offaly) and Queen's (Laois) rcds aren't in the database yet. Suggest you wait until they are. You have several alternatives to this: 1) Contact one of the IFHF affiliates in these counties and commission a search. 2) Visit an LDS Family History Library and view its microfilms for a fee. 3) Contact the National Library of Ireland for its earlier microfilms.
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 genforum msg.