Everytime I brew we have pizza for dinner. I cook my pizza on my Big Steel Keg at 500-600* and use a pizza stone every time. I am on the same pizza stone since 2006 and pitch black at this point from all the wood fired cooking.
The thing is you have to put the stone in as the grill is heating up not after it is heated.
Another tip, instead of using flour to keep the dough from sticking use corn meal. It works a lot better at letting you slip the peel under the pie and it adds a neat little flavor bonus.
EDIT: IF you want some pics and tips on cooking pizza on a grill go over to
Big Steel Keg Forum - Index and look around.