It is probably covered by the building codes in your jurisdiction and will be dependent on the depth of the mantle and possibly type of wood. I would contact your jurisdiction's building inspections division to be sure. You can also Google the question and get a number of different formulas. My own mantle starts about 12" above the top of the fireplace, but my mantle is soliid brick, and my fireplace is raised up off the ground quite a bit, so that wouldn't apply in your situation.

Well mine is raised up off the floor about a foot as well.

There is some formula I saw somewhere that you take 12" minimum, then if the mantle is wood, add 1" for every inch of depth of that mantle, so if the mantle is 6" deep, mount the mantle 18" above the top of the fireplace opening. It would be simple to call your city offices and ask about the code, though, to spare you heartache if you ever sold the house and that was flagged as out of code.