Warm 1/3 cup olive oil and the garlic in a small saucepan over low heat, about 30 minutes. Put a pizza stone or upside-down baking sheet in the oven; preheat to 500 degrees F.
Stretch the dough into a 12-inch round on a floured surface. Put on a cornmeal-dusted pizza peel or upside-down baking sheet. Brush the dough with 3 tablespoons garlic oil; top with the duck. Slide onto the hot pizza stone or baking sheet and bake 8 to 10 minutes.
Meanwhile, fry the egg sunny-side up in a skillet with the remaining 1 teaspoon olive oil. Top the pizza with the fried egg, arugula and parmesan. Season with salt and pepper. Drizzle with truffle oil, if desired.