She sounds a lot like my daughter. I am in the same shoes as you and I dont know what to do. I suffer from anxiety but it has become more extreme since I had my daughter. My daughter has been that way since birth and has just gotten worse with age. She is afraid of dying and fires. No idea why but she is. She also has a lot of friends and does alright in school but it does affect her alot.
I'd have her see a children's therapist. Her responses are very extreme, even given that she is just a child. Anxiety can be managed, but not by yourself. She needs a boost.
I suspect your daughter suffers from anxiety - probably generalized anxiety disorder. This anxiety disorder tends to "show itself" around eight years of age. I might suggest you google phrases as "GAD and children" or "anxiety disorders in childen" or "how I can help my child with anxiety" or similar words/phrases if you feel this might be the issue.
Anxiety is an inhertied trait and as such, if your daughter does suffer from anxiety, she was born with this predisposition. Do keep in mind that anxiety is a physical condition which results in parts of the brain over-reacting to perceived dangers; it usually is not caused from life experiences. This is why if you suspect anxiety is the issue, you should consult your family doctor. If he/she is unable to help you, then ask for a referral to a medical mental health specialist with experience in anxiety disorders. Do keep in mind that if anxiety is the issue, your daughter will not outgrow this nor will it go away (however, anxiety is highly treatable and can be "managed"). All the best ...
Could she have seen this behavior in anyone else in the family ?As you have been diagnosed with cancer she is probably worried about you and hears a lot of talk about it,I would definately get some professional help for her, and good luck with your battle against the disease..