It’s not a given that unbaptized babies go to Heaven but it’s also not a given they are in Limbo either. I do not believe either is a matter of dogma (is the doctrine of Limbo dogmatic?) so one is free to believe as one chooses in that regard as long as one doesn’t condemn the other for disagreeing. As far as I understand, that is what the passage from the Catechism states upthread.
Myself, I agree with Biggirl’s take on the issue: It doesn’t seem reasonable to me for a God who is not only all merciful, but “wills that all come to salvation” would allow babies (especially unborn ones) that are not baptized to languish in some Limbo. Limbo to me seems to be a construct of theologians who were not aware of or couldn’t imagine the horrors of abortion we face today, much less medical knowledge of miscarriages and the like.
Remember God is not limited to the Sacraments he instituted. He can save, and even bring to Heaven anyone he wants. Of course he can’t violate his own infinitely holy and just nature but just because we can’t imagine how an unbaptized person may enter heaven doesn’t mean it can’t be done. Who knows what happens at the moment of death for these babies, maybe in some mysterious way they are given the grace to choose God and are thus baptized by desire (as St. Dismas must have been). Or maybe they aren’t “baptized” at all (at least not as we understand baptism) because again, God is not limited to the Sacraments. (That idea, that God isn’t limited to the Sacraments, IS dogmatic by the way)
So again, we have a choice. I chose to believe God holds the sentiment, “suffer not the little children that they come to me” very seriously. Much more seriously than our limited idea of how an unbaptized baby fits (or doesn’t fit) into some Sacramental peg hole.
E.g., one must be born again of water and the Holy Spirit (Baptism)in order to be saved; but God can save anyone He wants to save, e.g. the unbaptized criminal crucified next to Him.
If we are aware that the Catholic Church was founded by Christ and contains the fullness of the means of salvation, then yes, it is morally obligatory for us to enter this blessed Church and to remain faithfully in her, participating with gratitude in the Sacraments instituted by Christ to give grace.
Yet one who, through no fault of his own, never entered the visible Church, can still be saved, because for God all things are possible.