Angora Rabbit
From wikipedia:
The Angora rabbit is a variety of domestic rabbit bred for its long, soft hair. The Angora is one of the oldest types of domestic rabbit, originating in Ankara , Turkey , along with the Angora cat and Angora goat. The rabbits were popular pets with French royalty in the mid 1700s, and spread to other parts of Europe by the end of the century. They first appeared in the United States in the early 1900s. They are bred largely for their long wool, which may be removed by shearing or plucking (gently pulling loose wool).
There are many individual breeds of Angora rabbits, four of which are ARBA recognized. Such breeds include, French, German, Giant, English, Satin, Chinese, Swiss, Finnish, to name a few.
What a cute pet it would make, don’t you agree?