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.
For Ann(ie) O'Brien B ???? in Co. Meath, there are 161 B rcds dating from 1756 and 67 M rcds dating from 1782. Assuming Annie was B 1842 +/- 4 yrs, there are 30 B rcds. A view of the B rcd(s) SHOULD show whether the mother's name was Julia.
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.