Your annotation states that Laurens
County is a county in South Carolina,
which I'm sure is true, but I think Joyce is referring to a county in
Georgia also called Laurens because earlier in the sentence is a reference
to the Oconee, which you correctly identify as a river in Georgia. Also,
the use of the word "doublin" later in the sentence is a reference to
Dublin, the county seat of Laurens County. The Oconee is a river that
passes though Dublin, Georgia in Laurens County.