A.D.
I think we have become a generation of scheduling play, which makes it harder and harder for our kids to use their creativity and self discovery. Let them learn how to entertain themselves, rather than taking it on as our responsibility.
My kids are older, but if I had to do it again, I'd banish the word "play-date" and allow my kids to be the directors of their own social lives, even at younger ages.
I'm not saying don't have friends over. But I'd be reluctant to "fill up a calendar". Take each day as it comes. Play with the neighbors. Be spontaneous. Coach your child on using the phone and calling up her friends to invite them over or out to play if she complains about being lonely.