Grilled pizza?

I pre cook the shaped pizza dough in the oven until almost cooked. Then I add the toppings and finish it off on the BBQ grill (Weber or sometimes Beg Green Egg). That way I can control when it will be ready, when I have space on the grill and it still has a wonderful smokey flavor.

If your using it directly on the without a stone. You do need to pre-grill before adding the topping. Cooking times will vary depending on how hot the fire is, and distant to the coals.
I put on the dough directly without a stone. (yes, it is rather 'free form'). Cook about 2 mins. Take it off and flip and decorate it. Pre-cook high moisture toppings (onions, peppers, mushrooms), add those quickly and return to the grill.
Here's a tutorial. http://slice.seriouseats.com/archives/2008/05/how-to-make-grilled-pizza-tips.html

If you do use a stone. Be sure to pre-heat it slowly. I've cracked a pizza stone in a Kamado (Big Green Egg Style Grill) because those things heat up very fast.

Optimally you have a real wood grill rather than a gas fueled one
A stone really helps. You can throw pizza dough on the grill Ala FLay but it comes out a misshapen mass of goo

Grilled pizza is amazing! Remember to treat the whole grill box just like an oven. I only have half of the grill hot and the other half is where I bake the pizza. Sometimes I pre grill the dough but if you stretch the dough thin enough and have a good hot grill box. You will be able to bake it similarly to a smokey oven.
Keep the toppings light and sparse. I use ripe tomato and olive oil for sauce instead of classic wet tomato sauce.
Take your time and be reactive to what the food is telling you. If it is browning too fast open the lid and let some heat off, if it is cooking too slowly pull it off and continue to let the grill heat up some more before putting the pizza back on. I use my pizza stone in the grill too, but you can use a sheet pan in there or just put the pizza right on the grill tines, a light pre grill will help prevent sag of the pizza through the tines when you add the weight of the toppings.