We just got back from camping with our 2.5 year old.
Things to bring Lots of baby wipes these double as a bath for alll of you to knock the dust off of you before you go to sleep.
Toys that can be washed.
a ground cloth to play on with toys They will still get dirty but not as bad.
Bug spray and sun screen, first aid kit, lots of bandaids.
Something to carry water in as it may be a walk. easy to prep meals. bringing things that mean very little cooking makes it easier to do. I like to bring pre cooked meat if it is an ingrediant. Like costco chicken boned pit into pasta. We like to bring shelf stable milk. Juice and things like that are best if they are in individual containers. Make sure there is food your little one will eat. also stuff to wash dishes.
Sleeping bag and air matresses, folding chairs if you have them, a hammer or something to drive tent stakes, flash lights to include one for the little one to play with (I have an Ikea rechargable night light for this purpose) Camera, flip flops for running to the bathroom in, a jacket no matter how wam it is supposed to be, think late night bathroom runs. knit hat for nights if it gets cold and you dont have much hair.
Portable high chair if you have one already. if not dont stress ablout it.
Things not to bring: Power anything unless you know your campsite is equiped, or you can charge it with your car, large ammounts of toys (dirt and sticks are going to be more fun) Simple is better. Work, email, cell phone (use only for emergencies)
PS a great tip we have used is when you get your camp site walk your child around and show them it and land marks of where they can not pass (like do not go past this tree that has fallen) make them large and noticable remember from their perspective all trees are big, rough tall.
We also like to give our little guy jobs. hold these tent pegs, take this to the tent, help find...) keeps them near and busy and they feel great because they are helping.
Lastly, dont take yourself or camping to seriously. Have fun. If you forget something there is usually a campstore or town not to far away or you can do without. Dirt happens, it is part of the fun.