Jennifer Oleniczak, Founder and Artistic Director of The Engaging Educator
If she wants to go, she's probably thinking of this academic camp in a very different way than a traditional school environment.
Yes, it's an academic camp that probably isn't getting her outside, or running around as much as an athletic/adventure/arts/special interest camp. But her desire to go shows that it's a special interest, so it might be best to view it as a traditional camp. It's not as if you are making her go, or suggesting that she go - and it doesn't sound like school is suggesting she go as well.
Does she have this opportunity in school? If not, this is also best viewed as an extracurricular activity - something she uses as a break from the academic side of things, even though it's categorized as an academic camp.
If you are concerned about burn out, it might be best to make sure the time surrounding camp is a complete departure from anything academic, and completely immersed in activities that are physical - the complete opposite of academic.