Can I go pick my daughter up and bring her home from a different state if we have no court orders for child custody?

I would highly recommend that you seek legal counsel to facilitate a court-ordered custodial arrangement that would provide for a specific visitation schedule. Proceeding without a court order leaves room for ambiguity and misunderstanding. In Arkansas, if you were never married to the mother of your child, you will need to initiate a paternity action to establish your legal rights as a father. Such an action would result in a court order providing for a specific custody arrangement along with child support and visitation.