Like Kalypso, I was also very much like your DD as a child. I used to worry terribly that my parents would be killed in a car crash, I used to not go round to friends houses unless I could get dropped back by friend's parents as I would be too worried about my own parents coming to get me. My dad often got held up at work and I remember sobbing in my room when he was half an hour late - I found in a notebook years later where I had written Daddy, pleeeease come home soon. I remember it was really very distressing for me. I was incredibly worried that there was going to be a fire in our home in the night, used to get the fire alarms checked every week, used to practice my escape route(!) Worried about being kidnapped in the night, the list went on and on.
I was also a perfectionist, an intelligent but very sensitive child; I thought very deeply about things, and I used to watch the news everyday from a very young age which used to add to the fear. In infant school I remember after the shootings in Dunblaine being terrified that this would happen to me.
Unfortunately I can't say that this hasn't had an effect on me as I've grown up, I have had serious bouts of depression, anxiety and anorexia, all of which I think stem from worrying far too much and feeling so out of control. I think what can happen with sensitive children (certainly what happened with me) was that I had empathy and skills to feel terrible about things that were going on in the world, I could understand how awful pain must be - but I was not old or mature enough to be able to comprehend that things make the news becuase they are rare, that misery sells papers, that yes, it is extremely sad when people lose their parents but you can, and will, survive.
I think with your DD a lot of loving patience is what is needed (not saying you're not doing this already), a lot of reassurance - make sure she feels that you are not belittling her fears - they are very real to her and only maturity will help her in time. I think a Cognitive Behaviour Therapist may be helpful for her, to equip her with some techniques that she can use to stop herself from thinking in cycles of worry and distress. Also, if she is watching a lot of news/reading the papers perhaps try tto cut down on that.
From a neurophysiological level, if the levels of stress and concern stay extremely high for long periods of time (years) - particularly in adolescence, when so many structural brain changes are occuring - it follows that your DD may learn patterns of negative thinking that will accompany her into adulthood and will be very hard to break. I know this sounds doom and gloom but I really don't mean it to be, but I really empathise with your daughter and I would hate for her to go through what I have been through. I think it is very important to address this asap, by therapy, by gentle love and understanding, and as much fun as you can fit in.
On a more positive note, certainly for me, my sensitive side also provides me with some of the best parts of my personality, and has given me some of the attributes that I am most proud of in myself. I also acheived extremely well at school, was kind and caring and never really caused anyone at school or home any problems.
Finally - have you looked up about your daughter possibly being a Highly Sensitive Child? It's not a condition or disorder, just a set of personality traits that often arise together. It might be worth checking out.
Sorry for the mammoth post, feel free to message me if you want any more information.