A.H.
My kids were also put in day care for the first time when my son was 2 1/2 and daughter like 14mos I believe. Now at first it was just 1-2 days a week and I was concerned about them getting sick myself. My son was sick twics with minor stuff and my daughter never got sick. Now they are FT so I be sure they are in bed earlier enough to get enough rest. They have been FT for 1mos and no sickness yet. Now I breastfed them both which does build their immune system. I give my son vitamins but not my daughter yet I will start her also though.
Also we bought a air purifier for their room to help.
Good Luck