Hi Megan,
Congratulations (almost) on your new arrival. I have an August baby too! I've traveled to Disney with an infant, and found the trip to be very manageable. The Baby Care Centers located throughout the theme parks were very convenient and helped facilitate a smooth trip. These are immaculately clean, quiet, air-conditioned areas where you can nurse, feed, change diapers and, if necessary pick up necessities like diapers and formula. The rooms have comfy rocking chairs, are private, and a great place to take a break with a baby. If you'd like some information on the centers, click
HERE.
Other tips for traveling with little ones include bringing a comfortable stroller that reclines, has a large canopy (to protect from the sun, and provide a good nap spot) and bring along whatever "baby gear" you need including snacks, sippy cups and or bottles, and little toys for the stroller.
While your little one may not remember his/her trip, you will surely have a photo album filled with wonderful memories. Babies are permitted to "lap ride" many attractions, including It's a Small World, Peter Pan and the Many Adventures of Winnie the Pooh. My little guys loved gazing at the bright colors and listening to the music on each of these attractions.
Have a great trip!