There is an important distinction that not everyone who goes to heaven receives an equal reward and not everyone who goes to hell receives equal punishment. This is alluded to by our Lord in his parable of the talents: “And that servant who knew the will of his lord, and prepared not himself, and did not according to his will, shall be beaten with many stripes. But he that knew not, and did things worthy of stripes, shall be beaten with few stripes. And unto whomsoever much is given, of him much shall be required: and to whom they have committed much, of him they will demand the more.” (Luke 12:47-48)
This is the basis of St. Augustine’s famous statements that the unbaptized infants in hell suffer the least of all the fires. They do not have any claim to eternal life, but they have no sins to be punished for. But if they don’t go to heaven, they must go to hell.
There is also the necessity of grace for eternal life. “Amen, amen I say to thee, unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God.” If infants do not receive this new birth, then of course they cannot enter heaven. It is possible that infants can be sanctified in the womb (such as the Virgin Mary and Jeremias) or I grant that it is possible what Feeneyites often say that an angel could secretly baptize someone at the hour of their death, but the established means of sanctification by Christ is the sacrament of baptism. It wouldn’t be right to presume that all infants are assuredly as privileged as the Mother of God.
There is also what St. Paul says in Romans 6 about the Fall. For example, “But death reigned from Adam unto Moses, even over them also who have not sinned after the similitude of the transgression of Adam, who is a figure of him who was to come.” It seems to me that this certainly applies to infants then.
I am inclined to say that unbaptized infants go to hell but they suffer no punishment (basically the idea of limbo). I also acknowledge it is possible that God can sanctify them in extraordinary ways.
I strongly recommend reading this if you haven’t already.
vatican.va/roman_curia/congregations/cfaith/cti_documents/rc_con_cfaith_doc_20070419_un-baptised-infants_en.html