Hi Paul,
My family and I love a stay at
Bay Lake Tower at Disney's Contemporary Resort. With children as young as yours, the proximity to Magic Kingdom will be wonderful. You can even walk to Magic Kingdom in under ten minutes!
At Bay Lake Tower at Disney's Contemporary Resort, you will be given a list of recreation activities when you check in. Be sure to look these over for things that your little one might enjoy. She might enjoy some of the activities held at Bay Cove Pool. There is also a splash pad area at Bay Cove Pool that she will probably love, and the pool has a zero-depth beach-type entry which is great for little ones. You can also take advantage of Community Hall, where you can enjoy crafts and games. Since she is so young, you might need to help her with many of the activities, but she will probably enjoy doing them with you.
As for your time at the theme parks, I believe that there are great attractions for toddlers at each park. At Magic Kingdom, she might enjoy classic attractions such as "it's a small world" and Peter Pan's Flight. At Epcot, she may enjoy interacting with Crush at Turtle Talk with Crush, or coloring at the Kidcot Fun Stops in World Showcase. Disney's Hollywood Studios is the place to go if she loves the characters from Disney Junior. Disney's Animal Kingdom is great for the animal-loving youngster as she can see exotic animals on attractions such as Kilimanjaro Safaris.
I suggest that you try to keep her on the schedule that she is used to as much as you can. If she is used to a nap in the afternoon, letting her take that nap will likely make her happier overall.
I hope that this gives you some ideas for your trip with your toddler, Paul. Please do not hesitate to ask if you have any further questions!