First complete cesus for Ireland is 1901- it and 1911 are online:
http://www.census.nationalarchives.ie/search/www.familysearch.orgThe birth you found was for Londonderry city:
Hannah Stewart born 7 Sept.1865 Londonderry (city) (page 197 in civil register)- parents- Joseph Stewart & Ellen
Mcginleyalso-
Charles Stewart born 7 Nov.1863 Beith, Ayrshire- same parents
There's also an extracted birth where the original names fit-
Isabella Stewart born 16 May 1859 Neilston, Renfrewshire- parents- Joseph Stewart & Helen Mckinlay
and Mary (1857), Helen 1867
Suggest checking for all these children in Scottish census records to determine which if any might be related to you.