Preheat oven to 425 degrees, Grease the donut pan.
In a medium bowl stir together flour, sugar, baking powder, cream of tarter, nutmeg, cinnamon, and salt.
Add in the milk, egg, and vanilla. Stir until just combined.
Gently stir in the diced peaches.
Spoon the batter into the donut pan. Alternatively, use a piping bag or zip top plastic bag to pipe the batter in. This helps to get the dough into the donut pan evenly and cleanly.
Bake for 8-10 minutes. Donuts should spring back to the touch.
Let cool in the pan for 5 minutes, then remove from pan onto a cooling rack. Cool completely before icing.