Do we need to have a written custody Order?

Yes.  Even parents who are very amicable and communicate well benefit from having a custody Order in writing.  By having your agreement made an Order of court, parents are given a forum to have issues with the arrangement heard and addressed if necessary, and your custody agreement will protect both parents and the children from the strife that can arise when an agreement is not formalized in writing.  Parents can keep their Order flexible, but know that their Order will control in the event of a disagreement.