My husband and I went starting taking our daughter camping with us when she was 1. Our son's first camping trip was when he was 3 weeks old!!! It is totally possible. We camped at a forest preserve close to home just in case we needed to leave (which we did with my son because it started storming and our tent leaked).
I recommend bringing an air mattress and sleeping bags, a small fan (if you can get a camp site with electricity), plenty of healthy snack foods, a magnifying glass to look at bugs, and a jar with holes in the lid to catch lightning bugs (release them quickly so they don't die...that is quite tragic for a little girl). Pack all of your food and clothes in plastic rubbermaid bins. It will keep them dry if it rains, and keep animals away from your food. And if you ever go camping while potty training, bring your toddler's potty chair in the tent with you.
Toys can be optional...there are so many fun sticks, rocks, plants, etc to look at you don't really need toys. We bring a couple of my daughter's dolls, bubbles, and a ball to kick around. Plan on some nature walks too.
We normally take a fire starter log just to be sure we can get a fire started quickly. Marshmallows and brats are fun, but make sure you have a long enough stick for your daughter. She will probably want to help "cook" them.
Have fun!!!