I experimented cooking a small pot of rice on a grill in my fireplace. It was more like a trial and error thing. Finding the not so hot spot to let the rice finish cooking without burning was the problem for me. That's probably going to be your problem too. I ended up leaving a minute crack in the lid to let lots of heat pressure escape so it wouldn't burn. That's about all I can offer.
The biggest problem with a wood fire, especially for a small pot, is getting very low heat under the pot for the rice to cook. I have never used an open fire, but when using a propane burner, I have the fire turned all the way down to low for the rice to cook. I have found that cooking small batches leaves much less room for error in the time/temp/technique equation. My 5 pound rice recipe is much more forgiving than my 4 cup rice recipe as far as getting the rice "right" goes. I honestly would try out a small pot first on a burner or stove where you can control the heat. If you really want to do the open fire thing, you need to make sure you have a much smaller set of coals under the pot for the simmer than you did earlier for the boil.
Just my opinion. I am an amateur cook at best, but I do cook up a large pot at least once a year at an LSU game for a crowd. The 5 pound bag recipe over propane has never failed me.
I've never cooked a mini pot but always wanted to try. As mentioned, controlling the temp would be the main issue. If I were to try, I would have a separate larger fire to generate some coals and cook only with the coals using a pot stand that would allow me to contain and control the heat. But as I said, I've never really cooked a mini pot.