http://unamsanctamecclesiamcatholicam.blogspot.com/2011/04/infants-who-die-without-sacramental.html

The 16th-century theologian Cardinal Thomas Cajetan, in his commentary on Thomas' Summa, stated,

    "that children still within the womb of their mother are able to be saved . . . through the sacrament of baptism that is received, not in reality, but in the desire of the parents."

St. Bernard of Clairvaux, a 12th-century theologian and a Doctor of the Church, wrote to a couple who had suffered a miscarriage,

    “Your faith spoke for this child. Baptism for this child was only delayed by time. Your faith suffices. The waters of your womb — were they not the waters of life for this child?  Look at your tears.  Are they not like the waters of baptism?  Do not fear this.  God’s ability to love is greater than our fears.  Surrender everything to God.”

A century earlier Jean Gerson, a prominent theologian, stated at the Council of Constance,

    "women great with child, and their husbands, to use their prayers for their infant that is not yet born, that (if it be to die before it come to the grace of baptism with water) the Lord Jesus would vouchsafe to sanctify it beforehand with the baptism of his holy Spirit.  Nay, who would not devoutly hope, that he will not despise the prayer of his humble servants that trust in him?  This consideration  is useful to raise devotion in the parents, and to ease their trouble of mind, if the child die without baptism; forasmuch as all hope is not taken away.  But yet there is, I confess, no certainty exists without a revelation."

This is nothing but heretical garbage.  BoD, assuming that it exists, due to its not being a Sacrament, can only work ex opere operantis and cannot be vicariously transferred onto an unbaptized infant.

It's more sentimental crap theology.  If the child died without Baptism, then there's a reason, known only to God, why this child died without Baptism.  Limbo, a state of natural happiness, would be a much better outcome for such a one than hell.

Much of this comes from the poor theology that was eventually corrected by Abelard which held that unbaptized infants suffer for eternity in hell.