Heat the grill over medium-high heat. Drizzle all the vegetables with the vegetable oil. Place the carrots on the grill, turning every 4 to 5 minutes, until you can pierce them with a fork (15 to 20 minutes total). Make a foil packet for the mushrooms and tomatoes and place on the grill, or use a grilling basket to cook for 6 to 8 minutes, until cooked through. Next, grill the onion and zucchini until tender, approximately 3 to 5 minutes per side.