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 Ann Dreelan B 1800-1920, somewhere in Ireland, with the parents' names unknown, I found 3 records, but NONE in Co. Wexford. Will leave it to you to visit the database and chase these rabbits to their respective counties.