Hi David,
We are all pretty biased over here at the Moms Panel, but my children have been coming to WDW since they were toddlers (first trip for one was at 6 months) and have had a magical time at every stage. We truly believe there is something for everyone.
To help you explore the parks, you can click
here for the Magical Beginnings Guide which highlights attractions of interest for the younger guests at WDW (just an fyi that Toontown is closed at the Magic Kingdom).
In addition to the many attractions,
character dining is so much fun for toddlers. Seeing their faces light up when they get a hug from Mickey or Winnie the Pooh is pure wonder!
If it were me, I wouldn't hesitate to take a 2 year old to WDW. You may even discover that you can't get it all done and will want to come back.
And on a personal note, we have travelled with my parents to WDW several times; the memories they made with their grandchildren were truly immeasurable. I hope you get a chance to build memories of your own with your grandprincess.