That individual is incorrect. The Church continues to encourage parents to have their children baptized as soon as is reasonably possible:
Catechism of the Catholic Church
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.
Code of Canon law
Can. 867 §1. Parents are obliged to take care that infants are baptized in the first few weeks; as soon as possible after the birth or even before it, they are to go to the pastor to request the sacrament for their child and to be prepared properly for it.
§2. An infant in danger of death is to be baptized without delay.