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