Statutory birth registration only started in Ireland in 1864 so you won?t find a birth certificate for her. You might find her baptism from church records but you really need to know at least one of her parents names to be sure it?s the right baptism.
If she was RC and came from Ballymena, then the parish records (Kirkinriola RC parish) start in 1848 so you may just scrape in.
I looked at the 1901 census for Co Antrim and McFarren etc. There?s only 1 person in the county with that exact spelling. The rest are spelled McFerren/McFerron/McFerran. The majority were Presbyterian but there were a fair number of Church of Ireland and RC too.
The RC parish records don?t appear to be on-line anywhere. A copy is held in PRONI (the public record office in Belfast) as well as the National Library in Dublin. A personal visit is required to access either set.