I would tend to find the positives in this... Doodling can be an effective means of note-taking for some people. Doodling can also be a means of enhancing one's concentration to absorb auditory information.
If it is your rule that doodling is not to be done on one's body, but on paper, you may wish to provide her with an ample supply of papers for doodling.
Advantages:
- Doodles on paper can be framed.
- They can be used to create greeting cards.
- They can be stored flat in a scrapbook or portfolio.
- They could become wrapping paper.
- Cropped sections could even be printed in a school year book.
