In my art therapy practice I sometimes am invited (by my client) to make art with them. It creates a therapeutic alliance, builds trust and helps to keep the space safe. One cooperative art making exercise I do involves my client and I taking turns adding to our cooperative art piece. This article talks about a beautiful trusted relationship between an artist and her 3 year old. Now I wouldn't necessarily call the artwork created by this 3 year old a "doodle", because the work is appropriate for a 3 year old child, but I do think that the final pieces are beautiful.
Have a look at the article!