In deep fryer or 2-quart heavy saucepan, heat oil over medium heat to 350°F. Separate dough into 8 biscuits. Using small round cutter, cut hole in center of each biscuit.
Gently place 2 or 3 biscuits in hot oil. (Biscuit holes can also be fried!) Fry on one side until golden brown. Gently turn with tongs; fry until other side is golden brown. Place on cooling rack; cool 5 to 10 minutes.
Meanwhile, in small bowl, stir frosting, butter and rum with spoon until smooth. Dip one side of each doughnut into glaze; top with chopped pecans.