How can we encourage our daughter as an artist?

I’d introduce her to communities like Conceptart.org to get a feel of what art as a profession is like.

It’s a community of professionals so the work is a pretty high caliber.

Here’s one simple idea and excercise. Ask her to draw what she Loves, then ask her to draw what she hates. Ask her objectively about the pictures. Don’t judge.

The Story of Art by Ernst Gombrich is an excellent introduction to art through the centuries.

If she is interested in animation, make sure to expose her to the different styles and techniques through the decades. In addition to the great CG animation coming from Pixar you have the hand-drawn Disney classics, stop-motion animation by Nick Park, some great animated films by Miyazaki and others from Japan as well as innumerable independent shorts from all over the world. There are lots of great clips available on Youtube. Some of the DVD's by Pixar and others have great making-of documentaries which show how professional animators work.