Some people feel the need to take the kitchen sink, and would put in 5000 lb cargo if they had the space.
You need lightweight dishes, basic cooking supplies, just enough cleaning stuff to get through for a while (broom, dustpan, dish detergent, maybe one basic disinfecting cleaner for the bathroom/kitchen). You don't need to replicate a full home kitchen.
And you don't need a full wardrobe---just basic seasonal clothes.
Kids don't have to take all the toys... they need to be outside, hiking or sight-seeing or playing in the mud.
Keep the outside cooking limited to marshmallows/hotdogs on a roasting stick, and you don't need tons of extra gear for that. You do want some reasonably comfortable lightweight chairs.
Your daughter is the perfect age to enjoy travelling and camping. Go and have a GREAT time!