Also the official teaching is contained in the Prior Roman Catechism, up to 1991.
Necessity of Baptism
If the knowledge of what has been hitherto explained be, as it is, of highest importance to the faithful, it is no less important to them to learn that the law of Baptism, as established by our Lord, extends to all, so that unless they are regenerated to God through the grace of Baptism, be their parents Christians or infidels, they are born to eternal misery and destruction. Pastors, therefore, should often explain these words of the Gospel: Unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God.
Infant Baptism: It’s Necessity
That this law extends not only to adults but also to infants and children, and that the Church has received this from Apostolic tradition, is confirmed by the unanimous teaching and authority of the Fathers.
Besides, it is not to be supposed that Christ the Lord would have withheld the Sacrament and grace of Baptism from children, of whom He said: Suffer the little children, and forbid them not to come to me; for the kingdom of heaven is for such; ° whom also He embraced, upon whom He imposed hands, to whom He gave His blessing.
http://www.catholicapologetics.info/thechurch/catechism/Holy7Sacraments-Baptism.shtml
Infants are not excepted from the necessity of baptism.