C.M.
I would not make this such a big deal. You would only be confirming her fears. If she saw a story about a dog attack, you wouldn't get rid of your own dog. If she saw a story about a car acccident, you wouldn't tell her she would not have to ride in the car.
Continue to reassure her casually (that's all she is really looking for). The only reason this is a big deal to you, is that adults have the fear of flying too.
Besides, things are more secure right after a threat. I flew one month after 9/11 and felt totally safe. If you relax about it, so will she.
I agree about kids never watching the news. My oldest is almost 14 and I'm still not comfortable with her seeing some of those stories. They'll be time for them to have to face the realities of the world as they approach adulthood.
Negative information should come to children on a "need to know" basis.