I recently read "The Emporor of All Maladies: A Biography of Cancer". I would not consider it appropriate for a six year old, BUT it is a tremendous source of information on historical progress on cancer treatment, how our understanding of cancer has evolved, and the current state of cancer treatment. As you are home schooling, you might find this a very valuable resource to read for information purposes. It was the best book I have read in years. You could definitely find some springboard areas in the book (cell biology and DNA/RNA/etc, how medications work against cancer, etc.) for science study with her, too.

I know this doesn't address her anxiety level, but being sure that the information you are providing is correct is best.