My son had to fly at 7 - It would not have been my choice, but we were visiting my mother, her brother died, and I absolutely had to stay and help deal with everything. It was a difficult situation anyway, plus my aunt and my 3 cousins were heavy smokers and I just couldn't justify keeping my child in that environment (I hated it myself). So I put him on a plane bag home to my husband. I was nervous (mostly that my husband wouldn't allow for the traffic and get there in time!), and I admit I shed more than a couple of tears when he trotted down the jetway with the attendant. When I spoke with him afterwards, I asked if he had been scared or nervous during the flight. He said, "No Mom, they check on you every 2 minutes!" I think most passengers are decent people, and the flight attendants can switch kids to a seat where someone has volunteered to help out. They won't allow her to sit in the emergency exit aisle, so that's nothing to worry about. Flights are so safe, and there's so much security in airports now anyway that there's so little risk. She won't be allowed off on her own, and she's old enough to speak up and ask questions of anyone in a uniform (security, airline agent, etc.).
He had some things to do on the plane and some snacks, and he was seated next to a very nice traveler who played a ton of "Connect 4" games with him! When he was taken off the plane and spotted my husband, he ran into his arms - even so, the staff said, "Sorry sir, we still have to check your ID." So I was happy about that as well.
Your daughter is older, more verbal, better able to entertain herself, and now there are things my son didn't have back then (cell phone, electronic games to play and iTunes to listen to), so there's even less to worry about. The plane escorts are really reliable and, in my experience, enjoying dealing with kids who are usually more fun than cranky, bossy adults in need of assistance. My guess is (and you should check), they will get her from one plane to the next in one of those golf carts, which may make her feel super important!
I'd consider taking her to the airport for a little bit of a dry run, have her read some signs and figure out where she's supposed to go. She won't need to do that on the actual flight day because she'll have help, but if she can navigate a little beforehand, you'll both feel more confident. Often, there are airline staff not just behind the counters but out where the people line up, to help "direct traffic" - so if you point all those people out to her, she'll see that she really can't go 20 feet without seeing an employee. And she will be escorted every step of the way - maybe you'll even see some kids doing the same thing and can point them out to her. With divorced parents all over the country, kids have been flying solo for many years.
I think it's a great opportunity for her to take on a challenge, succeed, and feel empowered. I think that's great for all kids, but especially for girls who get so many messages about being helpless victims.