Can we baptize our baby in the Church though we are not married?
Every Catholic parent has a duty to baptize their children in the Church. The code of Canon says:
“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 priest to request the sacrament for their child and to be prepared properly for it” (CIC 867 §1).
But to validly baptize your child, the Church demands that
For an infant to be baptized licitly:
1/ the parents or at least one of them or the person who legitimately takes their place must consent;
2/ there must be a founded hope that the infant will be brought up in the Catholic religion; if such hope is altogether lacking, the baptism is to be delayed according to the prescripts of particular law after the parents have been advised about the reason.
An infant of Catholic parents or even of non-Catholic parents is baptized licitly in danger of death even against the will of the parents.
However, as is the usual case in the Church, “An infant in danger of death is to be baptized without delay.” CIC. 867