In a medium bowl, stir together flour, 3/4 cup sugar, baking powder, salt, cinnamon, and nutmeg. In a small bowl, combine eggs, oil, and milk. Add egg mixture all at once to flour mixture. Stir just until moistened. Set aside.
In a large saucepan, combine blueberries, raspberries, blackberries, 1 cup sugar, the water, and tapioca. Bring to boiling. Pour hot fruit mixture into a 3 1/2- or 4-quart slow cooker. Immediately spoon the batter over fruit mixture.
Cover and cook on high-heat setting for 1 3/4 to 2 hours or until a toothpick inserted into the center of the topper comes out clean.
Remove liner from cooker, if possible, or turn off cooker. Let stand, uncovered, for 1 hour to cool slightly. To serve, spoon warm cobbler into dessert dishes. If desired, top with ice cream.