D.W.
I'm not aware of anything that's clinically proven to improve immunity though there are lots of products that make those claims (from Vitamin C to "immunity" enhanced cereals and yogurts).
We have 2 kids in day care. One is 3.5, the other is 23 months. The 3.5 year old was nursed the first year, was at our home with a babysitter until his 2nd birthday, and is hardly ever sick. His sister has been in day care since 9 weeks, has had 7 ear infections (tubes last year and 3 infections already this year). She's always sick. I could only nurse her 12 weeks because of needing to start chemo.
Different kids, different immunities.
I'd highly recommend being diligent (but not crazy) about handwashing and using sanitizers. I used to not be a fan, but they kept me from getting a potentially life-threatening infection during chemo when I had no immune system. At the time, I was working full-time (in pharmaceutical sales going in and out of doctor's offices all day) and had 2 kids in day care.
Good luck.
I do know from talking to my Oncologist's office this week that it's been a REALLY bad cold/flu season and everyone's been a little more sick than normal.