Zip, I’m [U]so[/U] [U]sorry[/U] to hear about your friend’s daughter. I hope that she will be feeling better very soon.
This web site has some nice hats as well as recommendations for what types of yarn are best tolerated for those undergoing chemo. As far as headcoverings go, you might get ideas about things to knit by looking at religious sites that sell headcoverings (for Orthodox Jewish women, conservative Christian women, etc.). There are some beautiful headcoverings on these sites that offer a fuller coverage that a hat may not.
This place has some very beautiful scaves, and this page on their site has many of beautiful ways tie them to offer a stylish variety. You might be able to knit her a either a square or rectangular scarf with some fabulous yarn and add some interesting trim like some of the scarves on this site have. I realize the items this site sells are already made and not knitted; I only listed this site because it is a good place to look for inspiration.
Sorry I can’t give ideas on specific things…a prayer shawl was my first thought, but I’m not creative enough to think of something that is more unconventional. :oops:
EDIT: You know what? I just thought of something. Maybe you can think about knitting her a snood? It would give the illusion of longer hair because it hangs down a bit, and you can dress it up with beads, etc. if you wanted. Also, it wouldn’t hug on the head too tightly (just the band around the head circumference would touch). Although most of the snoods I’ve seen are meshy, you can certainly knit one in solid fabric without holes. Here is a link to a sewn one that has a pattern; if you are able to knit one using the pattern as a guide, it might be helpful (I for one don’t know how to create or modify patterns, but I’ll bet somebody here can do it!).
Hope some of that helps!