Hi Rachael,
September (after Labor Day) is a wonderful time to visit if you are interested in some of the lightest crowds during the year. Once schools are back in session and the "summer rush" ends, the parks historically enjoy several weeks of low crowds and a "calm" atmosphere. We visited the week after Labor Day when my son was one, and I remember walking on to many attractions. In addition, we walked into several restaurants without advance reservations. (Please note that there is no way to predict crowds precisely, so if you are interested in a particular restaurant, I would still recommend making reservations.)
One other thing to note, if you are sensitive to heat, September (especially the early part of the month) is still quite warm in Central Florida. Over the past few years, Disney has offered some excellent specials in September, including Free Dining! While nothing has been published yet about September, check back at
www.disneyworld.com frequently for specials during your anticipated travel dates.
Have fun planning a trip!