Pizza on the grill? Why the hell not? --- Everything tastes better grilled, right? Pictured here is a pie I made on my gas grill. The missus said it was the best pizza she'd ever tasted. Being humble, I wouldn't go quite that far... But it was damned delicious.
First, get your grill as hot as it'll go. Then, the real secret is to cook the crust solo briefly on both sides to firm it up slightly before loading on the toppings. I cooked mine a minute or so per side, then took it off the grill to add the sauce and toppings before returning the pizza to the grill.
In the case of this pizza, toppings were tomato sauce made with San Marzano and heirloom tomatoes from the garden, fresh mushrooms, thin-sliced red onion, seven types of cheese (don't ask), homemade turkey "sausage," and fresh garden basil.
Put your grill to work making pizza. You'll love it.