In deep fryer or 2-quart heavy saucepan, heat oil over medium heat to 350°F. Separate dough into 8 biscuits. Using small round cookie 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 3 to 5 minutes.
Meanwhile, in small bowl, mix sugar and allspice; place on plate. While doughnuts are still warm, add to spiced sugar; turn to coat.