Hi fellow Michigander! We flew with our baby too, and WDW is the easiest place to bring a baby! Use the baby care centers! They are great! Each park has one and we made good use of them. They had baby food, formula, diapers, clothes to purchase. We bought some cute socks there and some bibs we hadn't seen elsewhere. If you're nursing, it was a very nice place to do this.
We also brought a very comfy (but not huge) stroller with a rain cver and actually used the rain cover a couple times. But then we are poncho people too, and bring those with us. We have very active older kids and decided to just keep going, letting baby sleep wherever we were. Yes, it meant someone sitting out from doing activities but we didn't mind. DH and I used this time to just talk and relax and it was actually very romantic! I know it sounds crazy, but it was a great time together. I know it depends somewhat on baby's temperament, but we decided, we were gonna just take her along and not sit in the hotel room. Have fun!