Can we baptize our baby in the Catholic church even though we are not married?

As Catholic parents, you have an obligation to have your child baptized. Code of Canon Law states, “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” (CIC 867 §1).

However, to baptize your child licitly, the Church requires that

[T]here must be a founded hope that the [child] 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. (CIC 868 §1)