I was going to bring up (and I see you mentioned it in a subsequent post) the need to save up for seminary. If you are struggling to pay for camp, seminary is a thing to keep in mind. In my circles it is completely normal for girls as young as 12 to start working at summer jobs with the plan that they are putting money away for seminary, several years down the line.
I think it really depends on your individual finances and also what your daughter would be using the money for.
Do you give her a realistic allowance so that she has money during the year to do normal social things with friends? If she needs to earn her own money to pay for things beyond basics that is something to consider. Realistically I wasn't able to work during school year because there simply wasn't enough time between homework, commute and music lessons (and practice) and yes - for normal socializing. I did work during the summers but I also needed the money to help pay for stuff I wanted even though I also got an allowance - stuff like getting birthday presents for may friends would not have been possible to get through my allowance for example.
If it is the only way to fund summer camp and your daughter wants the experience and it is discussed in advance, then asking her to fund 25% of cost is fair. But then realistically how much money will she have for the rest of the year and can she augment through working during school year and do you want her to - my parents didn't and there wouldn't have been time for me to do it.
This - my DD works half a summer and goes to camp the other half. But she uses her money throughout the year to pay for her social things. It's not only the savings concept that a child needs to learn, there's also the budgeting concept that very important for them. MY DD learns how to take the money she earns and budget it for the rest of the year. She seems to be doing a pretty good job of it.