I search the IFHF's online database at 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 almost non-existant. Many B/M/D events either weren't recorded, or haven't survived.
For Ed(ward) Moore B 1828 +/- 2 yrs, Co. Cavan, with the parents' names unknown, I found 0 records. Either the records didn't survive or haven't been transcribed yet.