Doctor Fuzzle is a doctor who takes care of Granny Bird when she sprains her ankle in I Want to Be a Doctor. Big Bird goes to Dr. Fuzzle's house and tells her about Granny Bird's accident, and Dr. Fuzzle immediately grabs her black bag and walks to Granny Bird's house to check her out. She checks out Granny's ankle, and helps her walk to bed. She bandages Granny's ankle, and tells her to come to the office the next day for X-rays.
There is apparently no charge for Dr. Fuzzle's services.