Baptisms in Ireland were usually the same day as the birth or the very next day. Once in a while if the infant was unusually healthy and the church was a few miles away, they family might wait until the following Sunday. But infant mortality was high, especially among the poor Catholics who were afraid an unbaptized infant would go to "limbo" or hell or purgatory. So the sooner the babies were baptized the more relaxed the parents would be.
Women were confined to bed for about ten days after their giving birth, a practice we know today is not healthy. So usually the father and the godparents would take the baby to church and the mother would not be able to attend her own child's baptism.
Catholics were about 85 percent of the population. The other 15 percent were their Protestant land owners, who lived in better housing, closer to town and with more resources. Infant mortality does not seem to be as high for this group, as they had a better diet, and better chances of medical care, not that medical care was very good back then. But religion was important, so getting the baby baptized in the Anglican church assured that they child could live a higher class life. Baptisms were probably, but not necessarily performed the first week of life, or at least the first month. Again, it may vary by the health of the child.
The Great Famine was mostly a problem for the Catholics, as the Protestant landowners would keep all the food they needed from the plantations they owned. So mother's and children usually had enough to eat, which would be essential for avoiding the malnutrition and disease that was rampant among the lower classes.