Can I request an emergency mediation hearing to discuss a custody and co-parenting plan?

You can file for pendente lite child custody/visitation/support determinations. A 50/50 agreement may not be the best situation for your child and you are probably correct that it will be difficult to get that agreement. I would suggest you also consult with an attorney as soon as possible to make sure you are protecting your rights and putting yourself in the best position possible for not only custody issues but your divorce in general. You can retain an attorney to help navigate this process before the 12 months of separation has occurred.