Yes it's an American Bittern, we used to call them Mud Hens...don't ask me why.
I've eaten quite a few Beavers when I was young as well as Muskrat. Beavers are good but Muskrat are excellent eating. I'm not a trapper but I've trapped them before, it is easy. When I was young I would use a .22, a shot to the head and that's it. If they're in deep water they sink but float after an hour