A "dogfish" (sometimes called a grennel or more commonly, a bowfin) are natural to most of the area lakes. They are far more common in the Bark River lakes than the Oconomowoc River basin ones, but by no means unheard of. I have never caught one in Moose, but I've caught them in the river across HWY C and in Lower Nashotah.
On the other hand, a "snakehead" is a non-native species.
If the fish you caught was actually a snake-head, the DNR would want to know about that right away, as that is a serious issue. There is some similarity to the fish, but knowing which one you had on would be kind of important.