Perkins' Plantation, variously called Judge Perkins or Mrs. Perkins's Plantation is located on the West bank of the Mississippi below Vicksburg approximately in the middle of Palymra Bend.
Plate 36-1 of the Atlas accompanying the Offficial Records show Judge Perkins place to be approximately 5 miles SW from New Carthage.
In Warren E. Grabau's Ninety-Eight Days, A Geographer's View of the Vicksburg Campaign, U of Tenn. Press, 2000, there is a map opposite the title page which shows Mrs. Perkins just below Somerset (Judge Perkins) at the mouth of Bayou Vidal.
On page 83 we find: " His [Grant's] intelligence sources had told him that there really were only two places along the river above Grand Gulf where there were good steamboat landings and enough dry ground for the camps of substantial numbers of troops. One of those was Mrs. Perkins's plantation, about three miles below Ione. . . . "
A Goggle search "Perkins' Plantation," will lead to a couple of hits in which Union regiments report of the area.