I'm not worried. The first time I took my family to WDW was September 22, 2001. We had been scheduled to go on the 15, but the planes hadn't started flying again yet. We flew down by Air Canada, and felt quite confident. The way I figured it, we were substantially safer flying on September 22, 2001 than we were any time before September 11, 2001. Security is a lot better now, and if someone were to try to hijack a plane, I don't think passengers or crew would be inclined to cooperate.
If it makes you feel better about having a family member be nervous about your flying, when I was eleven, my grandmother kept insisting that we were taking the train to Europe because she was so nervous at the thought of us flying there. And that was, well, more than a few years ago.
Ciao,
Mort.