Beavers are known for transmitting waterborne diseases like giardia and cryptosporidium. I've heard it said that if you have beavers, you *will* have at least those two present in the water. Giardia is aka Beaver Fever...that's how common it is.
That said, if you're fortunate enough to have on your property an abandoned dam that no longer dams water, you could have a great environment for permaculture.