Cook this pizza on gas barbecue?

I've not used this particular recipe with the grill, but I have done others similar using my trusty cast iron pan and the gas grill. You need a reliable thermometer on your grill, which will allow you to achieve and maintain the same temperature required if you were using the kitchen oven. On my three burner grill, that can be achieved using all three burners to heat up, and then turning off all but one. Set the pan on the un-lit side, close the lid, and leave it until the half way baking time point. Rotate the pan to expose the other side of the pan to the more direct heat, close the lid, and let bake for the remaining time. That's the best way to get a thick puffy crust that I know of. You may well have to experiment a bit with your own grill to figure out best times and identify hot spots, or the burner configuration best for keeping temperature. If you think of your closed grill as an outside oven, it opens up a lot of possibilities beyond burgers, brats, and hot dogs. You just need to know what the inside temperature is, and regulation of that temperature is a little more tricky because you do not have a thermostat to set.