Add the first 8 ingredients to a 1-1/2- or 2-pound bread machine according to the manufacturer's directions. Select the dough cycle. When cycle is complete, remove dough from machine. Punch down. Cover and let rest for 10 minutes.
On a lightly floured surface, roll the dough into a 14x8-inch rectangle. Cut lengthwise into fifteen 14-inch-long strips, each about 1/2 inch wide. Reserve 1 strip to form tails. Gently roll the strips into smooth ropes.
On lightly greased baking sheets, shape each rabbit by crossing 1 end of a rope over the other to form a loop, overlapping about 2 inches from each end. Twist the ends of rope once at the point where dough overlaps. Shape ends into points to resemble ears. Shape small portions from reserved strip into smooth balls for tails. Place a ball on top of dough at bottom of each loop, moistening if necessary to get tail to stick.
Cover and let rise in a warm place for 35 to 45 minutes or until nearly double. In a small bowl combine egg white and water; brush over rabbits. Bake in a 375 degree F oven about 10 minutes or until golden brown. Remove from baking sheets; cool on wire racks.