Another Problem

Two days ago I described a problem to me of a name on the Ireland, Births and Baptisms Index. Here's a second one. Mary was born on 3 June 1866 and given the surname McIlhagga. Her mother was Sarah Rea but no father is named. We may assume he was a McIlhagga. Mary was baptised at Broughshane, I assume in the First Presbyterian Church (where all the McIlhaggas were baptised, though it could have been in the Church of Ireland or even the Second Presbyterian Church). I wonder if I can find her father's name? There is no later marriage or death record that fits. Did Ireland have the equivalent of Bastardy Bonds which named the father so that he would pay towards the upbringing of the child? There is no Mary of the right date in the major McIlhagga family in Ballycloughan, Broughshane (mine). So where do I go from here? There is one Mary McIlhagga of the right age in the 1901 Census, living in Newtonards Road, Pottinger, Down, who was a Confectioner and who had a younger sister Elizabeth living with her, but I have no evidence that she was the daughter of Sarah Rea.