You can do the first 2 with a MTB with a BOB trailers. Probably not going to be too happy on singletrack trying to carry your camping gear in a baby carrier, but i'm not sure. You would probably want to look at the specs for baby carriers, and see if any are appropriate for off road use. Maybe check out the weight limits - my camping gear usually maxes out in the 40 pound range.

You could get 2 trailers, one for the kid and one for the gear.

One thing I wouldn't do, no matter WHAT is put my BABY in a carrier that wasn't rated for BABIES. (duh, and I know you didn't suggest that, but I'm just stating the obvious.)