Remove giblets and neck, and rinse turkey with cold water. Drain cavity well; pat dry. Place turkey on fryer rod; allow all liquid to drain from cavity (20 to 30 minutes). Rub outside of turkey with red pepper, if desired.
Pour oil into a deep propane turkey fryer 10 to 12 inches from top; heat to 375° over a medium-low flame according to manufacturer's instructions. Carefully lower turkey into hot oil with rod attachment.
Fry 1 hour or until a meat thermometer inserted in turkey breast registers 170°. (Keep oil temperature at 340°.) Remove turkey from oil; drain and cool slightly before slicing. Garnish, if desired.