Vermont's is actually on the walls outside of the visitor's center as you make your way to the camp.
This monument is for Clara Barton, who was part of the efforts after the war to ensure proper burial for all the dead and also that as many as possible were identified. Luckily the prisoner tasked to keep the records had kept a second secret copy for himself that he turned over to the party Barton was a part of. So we probably owe more to Dorence Atwater on this score but Barton receives much of the press, plus founding the Red Cross likely contributes to why she has a monument here.
A second woman memorialized at the park is Lizabeth Turner. She was president of the Women's Relief Corps, an auxiliary to the Grand Army of the Republic. She also served as life chairman on the Andersonville Prison board and died here.
The Women's Relief Corps erected this monument for the states that did not erect their own monument at Andersonville. Since then Vermont has erected the plaque shown earlier in the post.
This simple monument has the text of Logan's Memorial Day order on the right and Lincoln's Gettysburg Address on the left.