I know it's hard, but you are doing the right thing for your daughter! I hope she loves camp and you will see that all of the stress of these logistics is just temporary - after the first summer she will know exactly what she needs to buy/pack.
My girls sent most of their clothing to the camp laundry, and unlike the bad reputation most of it survived just fine, but they did hand wash their bras, pantyhose (worn only in Shabbos - knee socks for every day were fine in the camp laundry) and a few tops that they did not want to go in the dryer. They took a 3 drawer plastic storage container to camp to keep their stuff, and when they wanted to wash something they emptied one of the drawers and used it to wash the clothes with Woolite and hung to dry. Some of the bunk houses even had clothes lines for the girls to use, and when they didn't they hung the hangers of wet clothes from tree branches or whatever they could find. The girls do this during their rest time in the afternoon and it is totally not a big deal.