The inside of the Duomo will be about 20 minutes, the Duomo Museum is a 4 min. walk to its entrance, then inside the 3 floors will consume at least 1/2 hr. but a hour is better. A short, maybe 6 min. walk to the Bargello for at least an hour and a half, minimum time. Its about a 30 min.walk to the Pitti. There you could spend two days because of all the museums included. Of course the gardens and views from there need to be considered. You may want to consider walking to the Academia from the Duomo Museum. Its just a 7 min. hike. Take Via Ricasoli from the north side of the Duomo. While you are in that area don't miss the S.S. Annuziata Piazza, and on the other side of San Marco Piazza the S. Apollionia Last Supper by Castagno. Its a gem often overlooked.
I spent 10 years of 30 day summers there and as an art historian I teem Firenze "the Best"