The Catechism of the Catholic Church, which explains the what, why, how, etc…of Catholic doctrines, says this about Baptizing infants:
“Following St. Paul, the Church has always taught that the overwhelming misery which oppresses men and their inclination towards evil and death cannot be understood apart from their connection with Adam's sin and the fact that he has transmitted to us a sin with which we are all born afflicted, a sin which is the "death of the soul". Because of this certainty of faith, the Church baptizes for the remission of sins even tiny infants who have not committed personal sin.” (CCC 403)
“Where infant Baptism has become the form in which this sacrament is usually celebrated, it has become a single act encapsulating the preparatory stages of Christian initiation in a very abridged way. By its very nature infant Baptism requires a post-baptismal catechumenate. Not only is there a need for instruction after Baptism, but also for the necessary flowering of baptismal grace in personal growth. the catechism has its proper place here.” (CCC 1231)
“Today in all the rites, Latin and Eastern, the Christian initiation of adults begins with their entry into the catechumenate and reaches its culmination in a single celebration of the three sacraments of initiation: Baptism, Confirmation, and the Eucharist. In the Eastern rites the Christian initiation of infants also begins with Baptism followed immediately by Confirmation and the Eucharist, while in the Roman rite it is followed by years of catechesis before being completed later by Confirmation and the Eucharist, the summit of their Christian initiation.” (CCC 1233)
“The Baptism of infants
1250 Born with a fallen human nature and tainted by original sin, children also have need of the new birth in Baptism to be freed from the power of darkness and brought into the realm of the freedom of the children of God, to which all men are called. The sheer gratuitousness of the grace of salvation is particularly manifest in infant Baptism. The Church and the parents would deny a child the priceless grace of becoming a child of God were they not to confer Baptism shortly after birth.
1251 Christian parents will recognize that this practice also accords with their role as nurturers of the life that God has entrusted to them.
1252 The practice of infant Baptism is an immemorial tradition of the Church. There is explicit testimony to this practice from the second century on, and it is quite possible that, from the beginning of the apostolic preaching, when whole "households" received baptism, infants may also have been baptized.” (CCC 1250-1252)
“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.” (CCC 1261)
“Since the earliest times, Baptism has been administered to children, for it is a grace and a gift of God that does not presuppose any human merit; children are baptized in the faith of the Church. Entry into Christian life gives access to true freedom.” (CCC 1282)
“In the first centuries Confirmation generally comprised one single celebration with Baptism, forming with it a "double sacrament," according to the expression of St. Cyprian. Among other reasons, the multiplication of infant baptisms all through the year, the increase of rural parishes, and the growth of dioceses often prevented the bishop from being present at all baptismal celebrations. In the West the desire to reserve the completion of Baptism to the bishop caused the temporal separation of the two sacraments. the East has kept them united, so that Confirmation is conferred by the priest who baptizes...” (CCC 1290)
For discussion and a look at the Scriptural basis for Infant Baptism, check these posts out:
Scriptural support for infant baptism.
Infant baptism through the eyes of the old covenant