Hi Eileen, sorry this is a late reply, but if you are set on doing a concrete pad it does not need to be set deep at all. A floating pad for something as small as an oven would only need a concrete surface of 4" deep. I recommend digging down 4" as well and backfilling this with road base or gravel, then create a form with 2x4 lumber and pour your concrete pad.
Alternatively I would suggest not pouring a pad, but using larger rocks or urbanite from old cement walkways for the foundation. This works well and will save you money and labor. I still suggest doing the gravel base though. A small pad of concrete or stone, even if it heaves, will not matter much.
Are you planning a roof structure over this oven or just a water resistant finish?