I would really urge against trying to push all the way to Montgomery or Atlanta on that first day. That's more than 700 miles which is significantly more than we recommend when you're going to have to get up and be back on the road again the next day. Throw in the fact that you've got a puppy and will need to make even more stops than usual, and you could easily be on the road for 15-16 hours, and will leave you exhausted to to be on the road for 10 hours the next day.
We generally recommend that you limit yourself to a maximum of about 600 miles a day on a multi-day trip, and even less when you're traveling with with children or pets where you need to make more stops.
Birmingham is a little over halfway, and is 620 miles from South Bend. I could see you making it that far, but I really wouldn't try to push beyond that.