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 Pat(rick) Doolan (+variants) B 1805 +/- 2 yrs somewhere in Ireland with the father's forename unknown, I found 11 rcds: 4-1803 Kilkenny, 1804 Kilkenny, 1804 Meath, 2-1805 Kilkenny, 1806 Kilkenny, and 1807 Kildare. One of these MAY be for your ancestor - this era is very early for Irish rcds. You will need an exact DOB, parent(s) name(s), and/or placename(s) to pick which, if any, is the right one. Suggest you get info from his military service records. These can be found in the UK National Archives.
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.