Dylan, I've got good news and bad news. The good news is that, if you're trying to recreate a Pizza Pomodoro result, you don't have to hit blistering Neapolitan temps.http://slice.seriouseats.com/archives/2007/07/wellington-new-zealand-pizza-pomodoro.html
The bad news is that it's still hot enough that you'll need to insulate the oven. Start thinking about perlcrete for the walls, top and under the hearth.
Don't worry about a round interior. Just make a cube. Make sure to close up the front with bricks so your doorway is smaller than the width of the interior, and, as Gene said, make sure your door height is low- at least 3 inches lower than your ceiling. The top of the door should be 55-65% the height of the inner ceiling.
There's a chance you might hit temps that could melt foil. I'd build a doorway out of an extra two lengths of angle iron.
9" isn't bad. I'm not sure I'm in love with unmortared bricks standing on their ends, though. I'd probably stack the bricks flat so they're 9" high. I would also go with bricks for the ceiling rather than tiles. There's very little chance tiles will survive the heat you're going to be throwing at them.
You're using firebricks for this, correct?
Instead of a square, think of going wider. You want room for a fire next to a pizza.