Camp Dearborn rents boats and allows fishing on their little lake. I never caught anything there. It is in Milford (Oakland County, at the edge of the Detroit metro area).
I'm not sure what you mean by "southern" because growing up in Michigan that means south of a line from Bay City through Clare to Ludington, and if you are thinking "south of US-12" or "south of I-94" that doesn't cover many of the places I've actually camped. Almost any worthy campground in Michigan is on a lake, and so are many RV parks, or at least close to a lake. But Camp Dearborn is the one I know about.
Where my family is (Oakland, Wayne, Washtenaw, Ingham, Clinton and Genessee counties) I have reports that it has rained a lot but not flooded. I don't know how flooded you are where ever you happen to be in Indiana. My sister in Genessee county is complaining about how muggy it is from the recent rains. No guarantees, because all it takes is a thunderstorm cell to be stalled somewhere for thirty minutes and you will have a local flood.