I haven't lived in Wisconsin for 20 years, but last time I was there, deer gun season is the 10 days surrounding the week of Thanksgiving + the weekend before and after. October weather in Wisconsin is usually very mild but you can have some residual summer heat or early cool down. Make sure you can handle temperatures into the 30's. Though rain is not common it can always happen. Make sure to follow the weather as your trip approaches.

Black bears are not much of a problem along the ice age trail as far as I have heard. Bears are actively hunted in the area so tend to be pretty standoffish around humans.

I am not the most knowledgable about hiking with dogs, but if you are athletic and plan to do long miles be aware that dogs are not designed to travel as far as people can. They seem much more athletic than us, but they are made for speed and long naps. Trying to have your dog hiking all day can be dangerous for them.