In a 1 1/2- or 2-quart slow cooker, combine carrots, celery, corn, onion, garlic, rosemary, and 1/4 teaspoon pepper. Top with chicken. Pour broth over mixture in cooker.
Cover and cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3 1/2 to 4 hours. If no heat setting is available, cook for 5 to 5 1/2 hours.
Meanwhile In a medium bowl stir together flour, cornmeal, baking powder, and salt. In a small bowl combine egg white, milk, and oil. Add egg mixture to flour mixture; stir just until moistened.
If using low-heat setting, turn to high-heat setting (or if no heat setting is available, continue cooking). Transfer chicken to a cutting board; cool slightly. When cool enough to handle, cut chicken off bones; discard bones. Chop chicken; return to mixture in cooker. In a small bowl, combine milk and flour until smooth. Stir into mixture in cooker.
Using two spoons, drop Cornmeal Dumplings dough into four mounds on top of hot chicken mixture. Cover and cook for 20 to 25 minutes more or until a toothpick inserted into a dumpling comes out clean. (Do not lift cover during cooking.).