Here is the info. 1500 acres of hunting in the state park. I am not sure about the rest of the lake as it is under jurisdiction of the US Army Corps of Engineers.
Wayne Fitzgerald is around 3000 acres. Fairly flat ground (southern Illinois flat, not central Illinois flat). There are big deer there (150 inch plus), you just have to be willing to hunt areas that are not as easily accessible to foot traffic.
Begin by contacting the state park, as there are additional rules that apply. I camp there a couple of times a year and it is a really nice place. Not sure if the showers are open in November, but it is the best place I have ever camped.