If there is a custody petition, the court can order overnight visits if it determines that such visits are in the best interests of the child. Of course, that also means that court can determine that overnight visits are not in the best interests of the child and decline to award them. There unfortunately is no bright line rule that says a child of a certain age should get overnights at any particular age. It is all about the particular judge making the determination based on the evidence presented and considering the statutory factors that comprise the "best interests of the child" to determine what is appropriate. If you go to court, there is no definitive answer, but an experienced attorney might be able to give you a better answer given the general views of the bench and how they tend to decide cases like these, assuming the bench is predictable enough.
Yes, the court can order overnight visitation if it is determined that such visitation is in the best interests of the child. The fact that you're nursing is an argument as to why overnight visitation may not be appropriate right now, but it will not be dispositive on the matter.