I also do cornbread in the dutch oven too. I use a 6 inch small pie tin. I use a cornbread mix I get at Winco in a bin. I add some eggbeaters (instead of whole eggs) and a water to make a nice mixture, not too wet. Bake until knife comes out clean in the middle (about 20 mins last time – depends on heat of the coals.)
My trick for this in my oven is to place the pie pan on the what is usually a lid holder (the dark tripod thing it is sitting in in the picture.) That gives space and air under it. Don’t put the pan directly on the bottom of the oven! It’s an oven, after all.