First, to ease your mind, you can likely safety pin the zippers together so your daughter can't get out without a lot of fuss and effort. Just run the pin through the holes in the zipper tabs.
Depending on where you camp,(mosquitos!) some insect repellent and citronella candles or incense punks will help keep bugs away.
I also bring extra plastic bags for trash.
My biggest concern is usually making sure I have enough clothes for my son. Pack layers, because the day can go from hot to cold fairly easy. We also pack rain pants, just in case.
Some campsites have places to buy wood for fires; or you may need to haul it in. This is worth checking out. Same with basic fire tools.
Do you plan on eating/doing dishes with the RV folk? If not, double dishpans; one for washing, one for rinsing. Towels to dry dishes.
And lastly, stuff for your daughter to do. I prefer to bring more simple toys for my son, who's about the same age. Jump rope is great, a ball if there's space (frisbees tend to fly into other people's campsites, not so great), bubble stuff, and think about what else she might like to do. Card games, travel games are good. A few good books. Paper and markers or crayons--with crayons you can do nature rubbings of the local vegetation.
If you are looking for other nature activities she can do, consider borrowing this book from your local library: Mudworks by Mary Ann Kohl may give you a lot of ideas.
Have fun!