We own a couple of Reisenthel Market Baskets for use around the house for books and magazines; impromptu picnics; clean baby laundry; farmers market shopping; crochet projects; and anything else we can think of.
The design is great -- good looking, sturdy and the handle can collapse down for storage. We just stumbled upon the scaled down kid-sized Reisenthel basket so your little one can have one for herself. But even better than the original, the kids' version has a drawstring closure to keep contents inside. They retail for about $30.
Image: Reusable Bags