My advice after having made it once is, don't use a peel. I had an egg overboard after sliding my pizza onto the hot stone in the oven. Second piece of advice; take it out of the oven while your eggs are a little jigglier than you like, then let carry over heat take them the rest of the way while it rests for five minutes or so. This will keep your eggs from being over hard as well as save your mouth from being burned.
The roof of my mouth is smarting a bit as testimony of my impatience. It was worth it though.