I agree with the PP about Fort Wilderness. The boat between there, WL, and MK is fun and free, and at FW there are the stables, pony rides, bicycle rentals and paths, a playground, and even campfire activities in the evening. Trail's End is the restaurant there, which has a great dinner buffet with home style comfort food. You could even take a quiet walk through the woods to WL where you can explore that resort. You have all kinds of transportation options, since you can take a bus from either FW or WL to DTD or any park, or you could take boats to WL or the Contemporary.
We will have park tickets but I think our almost 3 year old will still enjoy a lot of those things. Have Fun!