Heat oven to 190°C. Lightly coat a 20 cm square or round baking pan with non-stick cooking spray.
Heat oil in a large non-stick frying pan over medium heat. Add onion; sauté until softened, 3 minutes. Stir in zucchini. Increase heat to medium-high; sauté until zucchini is soft and the liquid has evaporated, 7 to 10 minutes. Stir in ¼ tsp salt. Remove from heat.
In a large bowl, beat eggs, milk and remaining ¼ tsp salt. Add carrot, zucchini, cheese and dill. Spread in prepared pan.
Bake until quiche is just set in the centre, about 45 minutes. Transfer to a wire rack and cool for at least 10 minutes before cutting. Serve warm or at room temperature.