Hi Jennifer,
I've been taking my kids to the waterparks at Disney since they were one, and both are hooked!
Both waterparks have very well-themed areas for small children (under 48 inches tall). Blizzard Beach has "Tikes Peak", which is set up like a mini-version of the larger park. It has small slides,a tube ride, wading area and giant "sand castle" that are sure to delight your tot. This area is well-shaded, with wooden cabanas and many palm trees.
Typhoon Lagoon has "Ketchakiddie Creek" which is also a play area for little ones with slides, splashing pools and sand. Here, too, you can find shaded cabanas and trees.
Both parks are great. When my kids were smaller, we found that the kiddie area at Blizzard Beach was more elaborate and could keep them busy longer. Whichever park you chose, I recommend arriving early in the day. The water parks are very popular, and the "prime real estate" (i.e., shaded cabanas,
picnic tables, etc.) tend to be secured early in the day by anxious visitors. While people come and go during the course of the day, and space frees up, if you want a place to call "home" for the day, I'd definitely go early.
Have a great time!
Tanya