I have been doing some for my SIL. I am using a soft acrylic and / or a light weight merino wool blend. Here are a few links I found that also had childrens hats. You could also google knit childrens chemo caps. You could also suggest to her a knitting forum.
http://www.headhuggers.org/patterns/childpattk03.htm
http://www.headhuggers.org/patterns/childpattk02.htm
Here is a list of suggested yarns from another site which has some great patterns but none that I saw were for children.
https://www.knotsoflove.org/resources/