The single most important thing you could do to improve future portraits would be to light the subject from the side, with only one light source. The light shouldn't be exactly to the side, but rather at about 45 degrees and up 45 degrees. This can be artifical light or a window.
I highly recommend you read the many threads on the forum about how to light your subjects. It will make a world of difference in all your work. A good place to start is in the "resource photo" section of the forum.
There are also a number of great books you should try to look at. Try this link:
http://www.portraitartist.com/bookstore/photography.htm
I highly recommend "Professional Secrets for Photographing Children." It gives a lot of tips that apply to any subject (not just kids) and the best part is that it includes simple effective lighting diagrams.
I don't see any evidence of backlighting in this portrait, but what appears to be a light outline around all the areas of hair. Backlight would show more of a directional quality to it, (ie just on the upper left edges, or just from the right) instead of being around everything as it is in this painting.
Good luck!
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