Do I have rights to apply for overnight stay with my 2 month old daughter

You have every right given to you by the child visitation agreement that the court approved.

If you have not gotten to court yet, there is no "right" except to file in court for those visits.

If you are the legal father you have every right to request visitation. The court will look at all the facts and rule on what they feel is in the best interests of the child.

However a 2 month old is kind of young for overnights.