Janey wants a piccolo, too!
Getting a piccolo is a great idea if Janey is enthusiastic about the flute. It doubles the opportunities she'll have for playing, and it provides useful training. If she's even half way serious about the flute, sooner or later, she's going to play piccolo.
Buying a piccolo is even hairier than buying a flute. Not only do you have the regular morass of brands and models to choose from, but you've got to deal with extra issues such as whether you'll get a wood, resin, silver-plated, wood-and-silver, or resin-and-silver type of piccolo. To top it off, you'll have to listen to Janey trying out notes not meant for human beings to hear, let alone play, on an instrument roughly the size of a soda straw. (Bring earplugs - music store tryout rooms are always tiny.) I'm definitely not a piccolo expert, so I'm not going to get into the different kinds and their qualities here, but I can advise you take into account where the piccolo will be used. If Janey needs it for marching band, you'll want a cheaper instrument that can brave the elements outdoors. If she's in concert band or orchestra, then you can splurge on a nice wooden piccolo if you like. (Wood is considered the best piccolo material, silver next, and resin / plastic the worst.)
One last note about piccolos on a budget: cheap piccolos (i.e. made of plastic or resin) are HORRIBLE. They're horrible to play, horrible to hear, and frustrating for Janey because it's not her fault that she can't make it sound better. Piccolos are little beasts in general, but it helps to have the best instrument possible.
Piccolos are also as individual as snowflakes. Once Janey's narrowed it down to a specific brand and model, she should try as many piccs as there are available to try. Even supposedly "identical" models will sound different. That's good to keep in mind when brand-shopping as well - Janey shouldn't judge an entire brand based on how one piccolo sounds.