I just wanted to say that I have always, since I was a young child, been worried about dying. Not in a debilitating kind of a way, but in a "smell the roses" kind of way. When I was a kid I was particularly scared about house fires and kidnapping. As an adult I'm more worried about traffic accidents and plane crashes. Again, not worried enough to alter my plans, but worried enough to make sure that I tell my kids I love them when they get out of the car to go to school and to always kiss them at night before I go to bed.
I have to say that I think, in my case, it is a result of being gifted. I have always been much more aware of everything in the world around me than most of the other people I know seem to be. Also, I have always been quite interested in the news and in reading, which often features people in precarious and unusual situations. Logically, bad things can happen, and your DD probably knows this.
The two things I can think of that might help your DD is to make sure she is not exposed to the news or to scarier books for a while, and to point out that, if she does see something in the news, it is in the news because it is so terribly rare and unusual and unlikely to happen.
It sounds to me, though, that you handled the situation well.
