My son was born with Syndatyly but it was with 2 of his fingers (the middle and ring finger on his left hand) and not his toes. We chose to have his corrected surgically because the way the fingers were connected, it could've affected future activities and he would never have been able to wear a wedding ring if not corrected. You will need to ask yourself if correcting the situation is purely cosmetic or if it will have make a difference in function. There is quite a bit of recovery time and if surgery is not necessary, why put your child through it?
My son's surgery was performed when he was 18 months old at Edward Hospital. Our pediatrician did not want to do anything until he was at least a year old because babies grow so quickly that it could affect the success of the process. I also chose to wait until he was walking effectively since I didn't want him crawling or falling and catching himself with his healing hand. Our surgeon was Dr. Laura Semba, who sees adult and pediatric patients out of Edward and Orland Park (we, too, have an HMO and she was who we were referred to - I've never had a bad referral out of Edward!). Edward has pediatric anesthesiologists as well. I love Edward hospital and would never hesitate to take my children there for surgery. It is close to home and they are amazing with kids.
This is an out-patient surgery but is not a simple "cut the skin and be done with it" procedure. The surgery lasted over 2 1/2 hours! It involves intricate tiny zig-zag cuts and skin grafting so that the wound heals with minimal scarring and pulling. My son was in a full-arm cast for a week afterward to prevent use of his hand and to keep it clean. We went back to see the surgeon so she could monitor the wound and scar formation for about 3 months too. We are very happy we chose to have this surgery done, but mainly because if it wasn't done, he would've had limitations down the road. Otherwise, I don't think I would've put my child through surgery unnecessarily. You need to do what you feel is best.
Please feel free to send me a message if you have any questions. Good luck with whatever you decide to do!