Bessey is likely a dimmunitive "pet" name for her proper christian name. This name may have been Elizabeth. Bess, Bessie, and Bessey didn't come into general use until the late 19th cent.
I research the Irish Family History Foundation's database. It contains 12,700,000 surviving rcds for abt 70% 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 30%.
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 Be(ssey) Doughty B 1830 +/- 4 yrs somewhere in Ireland with the father's forename unknown, I found 0 rcds.
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.