They have a really fun kiddie pool by the Hippy Dippy pool. I'd guess it's right around a foot deep. It has "water bubbler thingys" (don't know what they're really called) that gently spray water up. My kids went in it alone--they were 4,4,almost 3 at the time. You'd probably want to get in yourself with a one year old though. They also have the Goofy jet spray area, which is really neat too.
**Wanted to add: I'm sure your 1 year old could walk in it. It was not even up to the waist of my almost-3 year old, and he's short for his age. Your tots will be fine!