Kristin from Grandma’s Chalkboard shares a tutorial at Make It and Love It showing how to make a reversible bag for a little girl to carry. She suggests using a twill or a decor weight fabric so the bags will hold their shapes. If you have your heart set on a lighter weight fabric, such as a quilting cotton, you could probably interface to give it the body it needs. Go to Make It and Love It to find her tutorial.
[photo from Grandma's Chalkboard on Make It and Love It]