I do hand applique, in part because it is so portable. Many of my fellow quilters like to do grandmothers flower garden and field of diamonds (both are hex patterns) by hand. (I do those by machine, but somewhat larger than usual)
You can go to any of the quilt pattern websites for applique patterns, or download coloring pages to cut up for patterns. When my oldest was very little, I wrote a book about him finding a black unicorn. After I became a quilter, I made that story into a quilt for my grandson.
What does you daughter like? Is there a particular sort of image you could reproduce for her?
Something else that travels well is crazy quilt blocks to embellish.