According to the Catechism of the Catholic Church, paragraph 1261:
“As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus’ tenderness toward children which caused him to say: “Let the children come to me, do not hinder them,” allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church’s call not to prevent little children coming to Christ through the gift of holy Baptism.”
However, according to the Code of Canon Law,
Can. 868 §1 For an infant to be baptised lawfully it is required:
1° that the parents, or at least one of them, or the person who lawfully holds their place, give their consent;
2° that there be a well-founded hope that the child will be brought up in the catholic religion. If such hope is truly lacking, the baptism is, in accordance with the provisions of particular law, to be deferred and the parents advised of the reason for this.
My advice, for what it’s worth, is, by all means, discuss the issue of the baptism of her children with your co-worker but do so very gently. Your main concern should be in helping your co-worker become interested in returning to the practice of her faith. Once this is accomplished, she will desire the baptism of her children on her own. Perhaps Patrick Madrid’s book, Search and Rescue: How to Bring Your Family and Friends into - or Back into - the Catholic Church will give you some ideas about how to do this.
