Hello Jessica,
I'm tickled to be helping you with your first family vacation to Walt Disney World!
Traveling with a toddler can sometimes be challenging. But Disney really does make it easy for parents to take their kids on vacation. There's always a Cast Member around willing to help you out!
I definitely recommend using a stroller, even if your little one usually does not ride in one. There's a lot of walking involved. You can bring your stroller or
rent one at the parks.
With your tickets, I would recommend spending one full day at Magic Kingdom. Your toddler will love many of the attractions in Fantasyland like Dumbo, It's a Small World, and The Many Adventures of Winnie the Pooh. One morning, I would suggest hitting Hollywood Studios to see Playhouse Disney - Live on Stage and riding Toy Story Midway Mania. The next day, I would go to Animal Kingdom to experience Kilimanjaro Safaris and to see the Festival of the Lion King.
When we took our daughter several years ago, we split our Epcot visit into two evenings. We explored World Showcase at a leisurely pace, a welcome change compared to the busy mornings we had at the other parks. I'm also sure your toddler will enjoy The Seas with Nemo and Friends.
And just so you have it handy, you can find a list of Baby Care Centers
here.
Enjoy your trip!