If you are a single mother or father, the priest should welcome you warmly. The priest will probably ask about the other parent and whether it is appropriate for them to take part in the service. If the other parent is taking a part in the upbringing of the child, then it will be good to have them take part in the baptism. If you are living with the child’s other parent, or another partner, the priest will probably ask whether you have thought of getting married. This is not so much a criticism of the way you are living as trying to understand where you are coming from on this issue.
For many people the birth of a child is a good time to formalise their commitment to each other by getting married. If you have good reasons for not getting married (e.g. your partner doesn’t want to) then the priest should be happy enough to baptise your child.
