I search the IFHF's online database @ ROOTSIRELAND.IE. It has abt 19 million B/M/D and other records for MOST Irish counties. Records before 1863 are increasingly sparse. By 1800, they are nearly non-existant.
For Ellen McCarthy B 1835 +/- 2 yrs, somewhere in Ireland, with a father forenamed John and mother Marg(aret), I found 3 records. NONE are in Co. Wexford.