Simply because you both agree on getting a divorce does not mean that your divorce is uncontested. In fact, it is not even close to meaning that. Certainly there are ways to work it all out without litigation, but you need to have everything formally agreed to before that can happen. Very often, a person will believe that both parties have agreed, but when it comes right down to it, when everyone finds out what they are entitled to or what they will be giving up, a contested divorce ensues.
Even when both parties agree, the same elements of divorce actions exist as when a divorce is contested. A divorce, any divorce, must make determinations on child support, custody, maintenance, distribution of marital property and determination of separate property. Unless all of these issues are in a proper, formal writing or ordered by a court already, your divorce is not uncontested. In simpler terms, everything but the grant of divorce itself must be formally settled on paper. Then and only then will there be an uncontested divorce if you satisfy the requirements that entitle you to a divorce.
This does not mean that you are forced into a contested divorce. Instead, you must get all of the elements decided and on paper, duly executed by both parties. Then, you can move forward with an uncontested divorce. Your agreement, though, will have to be viewed by the court as fair and reasonable. Otherwise, the court can overturn the agreement and you are then in the position of dealing with a contested action. Though the court overturning an agreement would be rare, it is important to be aware of the fact that it can happen.
If you have child support and child custody orders from Family Court, but need to address the issues of division of property and maintenance, you can do your formal agreement on the latter two issues, and state in it that you want to continue the child support and child custody orders.
Absent a separation agreement already in place, you do not have an uncontested divorce. On occasion, even with that agreement, if the other side wants any terms of the separation agreement modified, then, again, you can end up in a contested action.
In short, you may find that moving forward with an uncontested divorce is a two part process. The first part being formalizing the agreement between the two parties in a fashion acceptable to the court. The second part would be the divorce action using that agreement as the terms of the divorce judgment.