So I am wondering - who wanted to sign up for the camp knowing that she has such a hard time away from home? The basic issue is trust - isn't it? Or the worry that something bad will happen to you and then she'll be separated from you forever.
My son who is 10 is a worrier (like me - he got it honest - what can I say) but I talk with him a lot about those fears that he has. Mostly for him it's missing his family and thinking that something bad will happen while he's away. But it's never prevented him from going away overnight. Maybe it's just more intense for your daughter.
Don't rush her. Why make her go away to camp and then count on strangers to comfort her. She may not even confide in anyone how bad she's feeling. Why put her through it?
Spend lots of time talking with her about her feelings and find out what she worries about. And then together you two can figure out how to help her deal with it.
If it's basic anxiety - teach her some relaxation techniques - deep breathing, focus ideas (think about something you really really like), calming music, etc.
If it's specific worries, play out the scenario that she's dreading - WHAT IF . . .
Like - OK, what if I get in a car accident and I die. You will be terribly sad - but you still have (name other family members who she trusts and counts on) and they will take care of you. If you haven't already done so, make out your will and show her who you've determined to be her guardian, who she lives with, etc.... Let her know that you take her concerns seriously and that you and she CAN take steps to deal with those unknown horrible scenarios that she allows to take over her imagination.
This is only my ideas and some of the things that I have done with my worry wart son. Best to you and your sweet daughter,
M.