It's hard to understand why people don't make homemade doughnuts anymore. In a separate bowl, cream together the shortening and sugar, then add the egg and pumpkin puree and beat well to blend. Gradually stir the dry mixture into the wet one until just blended together. Heat about 4 inches of vegetable oil in a large heavy pot to 360 degrees. Fry the doughnuts, a few at a time, in the hot fat until nicely browned on both sides, turning once during frying.
Transfer doughnuts to paper towels to drain.
Dust with confectioners' or granulated sugar while still warm. Add next 4 ingredients and beat at high speed. Stir in crushed cereal. Drop by level tablespoons onto lightly-greased baking sheets. Make an indention in the center of each with the back of a teaspoon.