GIMP is free, so you should start there. There is nothing wrong with conventional pencil and paper. Every digital artist I know of started drawing when they were young, but it is never too late to learn a new media. You should encourage this with pencil, pastels, charcoal, inks, watercolor, oils and any thing else you can afford.
Does she like painting, or line drawings? I would suggest GIMP, except I don't know it at all since I use Photoshop. Either one should be great for painting. For line drawings the vector format is better, as in Illustrator. Every digital artist in every walk of like (movies, advertising, games) is also a Photoshop user. All graphic artists should know Photoshop and Illustrator well.
BTW, Autodesk Sketchbook is free now and it supports vector drawings. It cannot replace Illustrator, but hey it's free!
If she sticks to drawing on a computer, or tablet, then you might consider two things. One is a drawing surface, like a Wacom Intuos, or Cintiq. I found Intuos to be a disconnect because you are looking at one surface and drawing on another. The Cintiq fixed that because it is also a display, but it is not a toy and not entry level either (expensive). There are other tablets and surfaces, but you should probably wait to see if she is still doing this in her mid-teen years.
EDIT: I don't know what there is in pre-teen tablets, but I bought a boogie board (LCD writing screen) for my son. It can be used for drawing also.
