Did she marry in England? if so, her marriage certificate should list her father's name & occupation (unless illegitimate) and an address.
It sounds as though little information is known about her (in England at least) but something like an old address book might give clues to relatives in N.I.
Very few recent records will be available online.
If she was born 31 Dec.1944 her death would most likely be registered in the Jan./March 1945 quarter.
The online civil registration index for Northern Ireland (
www.familysearch.org) only goes up to 1921 for Northern Ireland counties. GRONI (General Register Office Northern Ireland) also has a database online but birth records have 100 year restriction.
The latest N.I. census is 1921.