In bowl, combine rice, flour, sugar, baking powder, salt and nutmeg and mix well.  Add eggs and vanilla and mix well. 
Heat vegetable oil for deep-frying to 360˚F.  Carefully drop rice mixture by spoonfuls into hot oil and fry until brown. 
Remove with a slotted spoon and drain on paper towels.
Sprinkle with confectioners' sugar.

Serve hot.