Preheat the oven to 375°F (190°C). Grease a donut pan.
In a large bowl, combine the peanut butter and whole wheat flour. Mix until crumbly.
Add the egg and mix well to form a dough. If the dough seems too dry, add a splash of water at a time until it reaches a kneadable consistency.
Gently fold in the carob chips, making sure they are evenly distributed throughout the dough.
On a lightly floured surface, roll out the dough to about 1/4-inch thickness.
Use a donut cutter to cut out donut shapes. Alternatively, shape the dough into balls and press a hole in the center to form donuts.
Place the donuts on the prepared baking sheet, leaving some space between them for spreading.
Bake for 15 minutes, or until golden brown and set.
Let the donuts cool completely on the baking sheet before serving them to your dog.