How will I know if I have full custody of my daughter if I moved out of the state where I filed?

When you "filed for custody in Oregon," did you file a Petition for Dissolution of Marriage or a Petition for Filiation, Custody, Parenting Time and Child Support with the Circuit Court in the county where you resided at that time? Also, were you represented by an attorney? The problem I am seeing here is that if you only filed for child support with the state Division of Child Support, you would have an order that requires your child's father to pay child support but no court order granting you sole custody of your daughter. The history of the case you filed in Oregon, specifically the actual orders and/or judgment entered by the Court, would tell us what we need to know to answer your question.