Ok, I just tried to post this and I don't think it worked, so if I've just posted this incredibly long response twice, I do apologize.
I'm not actually a mother (I got signed up for this site when a friend of mine planted a tree in my honor, I think), so I've never responded to a question before, but this one reminds me very much of my own experience, so here goes.
I had periods of deep fear like this during my childhood, and I did not actually grow out of them as an adult. When I was 19, I went through a period during which I was terrified that an asteroid might obliterate life on earth. I was actually majoring in engineering and minoring in astronomy at the time, so I knew how silly I was being, and this made the whole thing even more irrational and frustrating. I could not control my fear, and once the physiological symptoms set in (pounding heart, cold sweats, stomachache, etc.) it would get away from me entirely and become an entity completely apart from anything my rational mind could say. I would hold my breath in the morning before checking the internet news, terrified that the front page story would be that scientists had discovered an asteroid hurtling towards earth and we all had a week to live. After months of lying awake at night and losing sleep due to my fears of death by gigantic space rock, I finally told my boyfriend about my fears. God bless him, he never laughed at me or called me silly, he just laid out the facts with regard to how unlikely that really is. Just having someone who supports me and doesn’t talk down to me when I have these fears has really been an enormous comfort.
The asteroid thing was not the last episode for me. I suffered a nervous breakdown during my first year of graduate school (at the age of 23). I had a displastic mole removed from my arm and became terrified of developing skin cancer. I literally felt like I could feel cancers growing in the moles on my body. I was in such a state of heightened adrenaline for so many days on end that I woke up at 2:00 am one morning, heart pounding and unable to breathe. I checked myself into the ER, where the doctors gave me sedatives. The next week I was diagnosed with generalized anxiety disorder and began taking antidepressants. I have been under psychiatric care since (the past 5 years). It has really helped me, as have the yoga and meditation classes I have taken. I see my fears now as part of the way I experience the world, and something that I can forgive myself for, live with, and control. I haven’t had an extreme episode since, but I feel like if I do I will recognize it for what it is and get through it. So what I’m trying to say is not that you should automatically take your daughter to a psychiatrist, but that you should keep it in the back of your mind that if these episodes persist into early adulthood it would be a good idea to suggest that she seek help. In the meantime, show her support and let her know that her fears are irrational, but also that that doesn’t mean that she herself is silly. Maybe help her try to find some ways to deal with the episodes. Reading fiction works well for me, since I apparently use the same part of my brain to visualize a story as I do to visualize how horrible it would be if whatever thing I’m currently obsessing about actually happened. Be someone that she can talk to honestly about her fears. I never felt able to discuss my problems with my parents, since they typically responded (it seemed to me) with a combination of dismissiveness about the irrationality of my concerns and worry that I was somehow abnormal. Also, teach her how to take care of herself (life skills like cooking, first aid, how to handle money, etc) and remind her that if something bad does happen, she can handle it. I’ve read that people with generalized anxiety disorder are typically very intelligent (extra brainpower = extra capacity to think up scenarios and worry about them), so I’m sure you’ve got a very smart little girl who will do great things one day! And even if this problem does persist, there is definitely light at the end of the tunnel.