To restate Catholic doctrine: Baptism is necessary for salvation, but the children who have died in the womb or after birth but before the age of reason without Baptism died without the Sacrament through no fault of their own. Original sin still remains on their soul but they could not have committed any actual sins. So, is it just that they should suffer in Hell? St. Augustine believed that children who die without Baptism would unfortunately have to go to Hell. Yet, as the Church has further understood this reality, this is not the case. Pope St. Pius X and other saints have disagreed and claimed that such children go to an special place called the Limbo of the Infants. The Catechism of St. Pius X states, “There should be the greatest anxiety to have infants baptised because, on account of their tender age, they are exposed to many dangers of death, and cannot be saved without Baptism.”
Pope Pius VI in Auctorem Fidei on August 28, 1794, particularly countered those who sought to deny the Limbo of the Infants when he wrote:
[Errors of the Synod of Pistoia.] The doctrine which rejects as a Pelagian fable that place of the lower regions (which the faithful generally designate by the name of limbo of the children) in which the souls of those departing with the sole guilt of original sin are punished with the punishment of the condemned, exclusive of the punishment of fire […] is false, rash, injurious to Catholic schools.
Here is the teachings of previous Popes and Saints.