In a large bowl, whisk together cornmeal, gluten-free flour, sugar, baking powder, and salt.
Add the beaten egg and buttermilk, and stir until smooth. If the batter is too thick for dipping, add a little more buttermilk to reach the desired consistency.
Pat the hot dogs dry with paper towels. Insert a wooden skewer into each hot dog, pushing it halfway through.
Heat the vegetable oil in a deep fryer or large pot to 350°F. Dip each skewered hot dog into the batter, ensuring it is completely coated.
Fry the corn dogs in the hot oil until golden brown and crispy, about 3-5 minutes. Drain on paper towels.