Pique: I see where your coming from, and in a way total agree, it is a disgraceful bias - sometimes - however, when the childs permanent place of residence is at the other end of the country, considering she will be of school going age, along with (presumably) full time residence with her mother for the last 3 solid years, its unlikely he would succeed, not because he is the father, but because of the circumstances and general living situation she has had with her mother. But I do see where your coming at this from, the precedence of mothers rights versus fathers rights. However, just because he applied to the Court, it doesn't necessarily mean he cares about his daughter.
It would seem that there would be a 'better solution' than "joint custody", a few weeks during the summer for Dad, every second xmas, things like that, rather than disrupting her day to day life. And, should the shoe be on the other foot per se, Father applicant, and he was in the situation of the mother. Mother in Dublin (presumably) little or limited access, Dad does all the primary work, schooling, day to day, my advise would still stand, I wouldn't worry.