I felt sorry for Averi and her shiny, bald cancer head so I thought of a solution. I think it works well.
Are you creeped out yet? I'll wait for you to stop laughing...
We currently have one of the world's creepiest dolls in our possession (thank you Stephanie) which is the same size as Kaili and sports handmade clothes, blinking eyes, and a wig. My sister-in-law thought that Averi's head might be the perfect size for the wig (notice how I'm not taking any credit for this) and it fit surprisingly well.
Averi even kept it on once I distracted her. I'm pretty sure Averi's going to wear it into the hospital the next time she is admitted. =P