I'm a single parent and got into camping with my now 4.5yo daugher a couple of years ago. I think she was just 2 the first time we went. I hated that trip, but that's another story.
One piece of equipment I can highly recommend is a good walkie talkie! I bought our first one about a year ago and have just upgraded to a more powerful one. Haven't actually tried it for camping yet, but am dead keen on doing it next time and wish I had previous time.
The great thing about them is that you can use them as a baby monitor. But they work on batteries as opposed to most baby monitors. That way you can sit by the neighbours' campfire or even use the amenities if they're closeby, but always hear them.
Now my daughter knows how to use them properly, I can also stay in touch with her if she wants to go visit a neighbours camp while I'm doing chores or go for a bike ride around the camping grounds. At home I even take them when we go shopping just in case I lose her!
Other than that, I think the important thing is that you explain the few important rules, but keep it to a few and make them very clear. Things like: never leave the esky or the tent open, no running near the campfire, no wandering off past certain boundaries, no leaving appliances switched on when not in use and whatever chores you want them to do, like collecting kindle or doing the dishes.
My daughter sometimes helps to put up the tent and she is surpringly helpful sometimes. But after a long car drive I don't insist if she doesn't want to.
I find it THE great thing about camping for kids: there are so few rules compared to at home. And that makes them much more inclined to follow those few rules you do insist on.