On page 22 of Kurt Vonnegut's darkly whimsical novel Breakfast of Champions, he claims that the word beaver meaning "vagina" originated among news photographers, who used it as a code word to tell other men that you could see up a woman's skirt from that angle. I don't know where he got that from, but I can't find any sources on that. The euphemism seems to trace back to 1910s British slang, when it referred to a man's beard. By 1927, due to the visual similarity, the definition got extended to female genitalia. The "beard" meaning emerged because of a resemblance to beaver pelts, and that word goes back to Old English beofor. Even earlier, beofor is from (through Proto-Germanic) the Proto-Indo-European root bher, meaning "bright" or "brown". Usage of beaver in language over time peaked in the 1850s, and the Vonnegutian definition is, in conclusion, erroneous.
Adam Aleksic, a freshman studying linguistics at Harvard University, has been described as the internet's sixth most famous etymologist. He has disturbing interests in words, vexillology, geography, board games, limericks, and law, and he loves writing about himself in the third person.
The Etymology Nerd