The Nikon 1 series is a good upgrade to a point and shoot. That's a great price if it comes with the kit zoom lens, and this is a fine system for a 14 year old.
A Micro 4/3 system is also a decent choice. The Panasonic G5 is widely available with a kit zoom for under $400, and it's a fine camera with a wide variety of good lens choices from Panasonic, Olympus, and others. We have a fairly complete m4/3 system at our house (4 or 5 cameras, maybe ten lenses or so.) It's my wife's primary system, and it was my personal/travel system until recently. I like the G-series from Panasonic for the built-in electronic viewfinder (the kind where you hold the camera up to your eye, not out at arms' length.) The kit 14-42 zoom is fine to start, and later you could add the 45-200 zoom for not much money. If she really starts to push into serious photography, I'd get her the Panasonic 20mm f/1.7 prime lens and have her use that exclusively for a while -- it provides a level of control over various photographic parameters that will help her learn and hone her technique.
Macro: A lot of zoom lenses offer a "macro mode" which allows them to focus on a close subject. However, if you want to truly get closeup photos, a specific macro lens is required. Not sure what the Nikon 1 system offers for that. The Micro 4/3 system has two macro lenses, one expensive and one even more expensive. The Olympus 60mm f/2.8 macro is $500, and it's excellent -- my wife has one and uses it all the time.
The key to all of this is to find a good teacher and have her out shooting as much as her interest allows.