1. Stir together first 5 ingredients.
2. Remove giblets and neck from turkey, and, if desired, reserve for another use. Rinse turkey with cold water. Drain cavity well; pat dry. Rub turkey evenly with 2 Tbsp. vegetable oil. Loosen and lift skin from turkey breasts with fingers without totally detaching skin; spread one-fourth salt mixture evenly underneath. Carefully replace skin. Sprinkle additional one-fourth salt mixture inside cavity; rub into cavity. Sprinkle remaining salt mixture evenly on skin; rub into skin. Place turkey on fryer rod.
3. Pour peanut oil into a deep propane turkey fryer, pouring 10 to 12 inches below top of fryer. Heat to 300° over a medium-low flame according to manufacturer's instructions. Carefully lower turkey into hot oil with rod attachment.
4. Fry 45 minutes or until a meat thermometer inserted in thickest portion of thigh registers 165°. (Keep oil temperature between 300° to 325°.) Remove turkey from oil; drain and let stand 15 minutes before slicing.