Hi Nicole,
Welcome home and what a wonderful vacation you will be planning!
Since you may want to concentrate on the Magic Kingdom, you may want to consider Bay Lake Towers which is at the Contemporary. You can walk to and from the Magic Kingdom and ride the monorail to Epcot. The location is great but I was not in love with the pool and recreation area especially for a 13 month old. Another option is the Wilderness Lodge which is beautiful. However, this is serviced by boat to Magic Kingdom and then buses to the other parks which makes for a longer travel time.
Two other options are the Beach Club and the Boardwalk. Both of these resorts are walking distance to Epcot and Disney's Hollywood Studios. You can also hop on a boat and not have to worry about collapsing your stroller. We stayed at Boardwalk, our home resort, when our children were in strollers and loved it. We would even take the monorail from the Magic Kingdom and walk through Epcot to catch the fireworks some nights instead of taking the bus. The Beach Club was not an option when my children were little but I would stay there if I could.
The other DVC properties-Saratoga Springs, Old Key West and Animal Kingdom-all use bus transportation to the parks. This makes your travel time longer especially if you want to return daily for breaks.
Wishing you a magical first vacation!
Beth