R.
Hi! I am relatively new in La Grange and I found an organization called LaGrange Area Newcomers and Neighbors. They do a lot of charity and social events. But, what first brought this to my attention was a weekly playgroup that they host as well. They meet every monday at a local church (I have only been to it once so far). i really enjoyed it and plan to go back. It was nice to meet some new people in the area too.
There is a $20 fee to become a memeber, but your first three events or playgroup meetings are free (just to see if you'll like it or not without having to pay up front). I haven't joined yet, but I most likely will. I will be going to this week's playgroup, but I'll be a little late. It runs from 9:00-11:00. When I was there last there were mostly toddlers 12-24 months--so your daughter would fit right in.
The organization has a website that will explain everything a lot better than I can! http://www.lagrangeil.com/LAGAN/index.htm
Hope that helps!
R. Blackstone