You'll be packing food and beverages for your family, not to mention a tent, sleeping bags, and an assortment of items like blankets, folding chairs and rain gear, so you'll also want to include a number of items necessary for meeting your dog's basic needs.
Pack plenty of food, treats and water (plus doggy dishes). Grab a few favorite toys, some blankets and towels, a bed and a brush. Dogs can get sunburns and injuries, so a doggie first-aid kit and sunscreen aren't bad ideas, and you might want to include a little extra dish soap and shampoo to clean the animals if they get dirty.
The weather (which you should check beforehand to make sure it won't be too hot or too cold for your canine) is also a good guideline for tailoring what you pack. If it looks like rain, a carrier could provide a refuge for your dog to stay dry. If it's hot, ask for a campsite with some shade. If it's cold, consider bringing warm accessories like dog boots.