As for the origins of the Beaver, here's a picture of the angry Beaver mom.  Don't fuck with a Beaver.

Where do ya think he is.... out with me! hunting beaver!

as  to where did  beaver referring to the female vagina... well that comes from either english or Czech origins... referring to "beaver pelts" or "bearded man" and techically refers to those organs covered in hair, but nowadays with all the hair removal (which I like) it seems odd to still use the term when the rug has been removed and replaced with hardwood flooring.