I was in girl scouts as a kid, as were both of my sisters. I was also a summer camp counselor when I was in college (week-long camping for brownies through juniors--I had the brownies groups for 3 weeks). I say if you are confident that she is mature enough to behave and won't have severe anxiety leaving you, this is probably the perfect age to let her go! The GS are heavily mandated, so there will always be emergency contact information, adult supervision, and it will be an awesome experience for her. Be sure that you let the troop leader (or whoever is in charge of this trip) know that this is your girls' first trip, that they have your contact info, and that you have theirs. Ask about their adult-to-kid ratio. Do NOT call in the middle of the trip just to "check up" on them! And, it may be hard, but try to put on your bravest, happiest face and let your girl know how proud you are and how she's going to have TONS of fun, etc, etc. Try not to let her see that you're so worried, or it might make her more anxious, or she'll hold back from having fun because she's worried about you. As a camp counselor, I saw many kids come in crying not wanting to leave, but as soon as mom leaves, they are the first to offer to help, explore, etc!
Good luck, I think this would be a wonderful experience for your girl!