It is true that most custody orders require advance notice of a move to both the other parent and the court, but you are saying that there isn't a custody order. Was paternity established? Does your daughter's dad pay child support? If the state administers it, you would need to let them know you are planning to move. Here is a link to information about the Oregon Child Support Program.
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Under Oregon law, a petition for dissolution of marriage must be filed in the county in which one of the parties lives. Since both of you live in Multnomah County, that is the only county where you can file.