Hi R.---I agree with other posts that talk about how every body is different and that it is difficult to compare how your 2 yr old developed with your 9 month old. His immune system simply is different.
You are right that babies get some of their immunities from breastmilk, but I do believe that that diminishes as time goes on. Being in daycare, he will be exposed to more germs than the stay-at-home baby, but, if there is anything positive to see in this, his own immune system is working on fighting these colds and will have his own immunity to those germs at an earlier age.
Some ideas to help strengthen the immune system. Be sure to eat a diet that consists primarily of fresh fruits and veggies, whole grains, legumes (beans), nuts and seeds. Minimize the consumption of animal products (anything that has a face), using it as more of a side-dish or flavoring for soups or stews. This includes diary, as dairy is highly allergenic and can impact how the immune system functions. Too much animal protein leads to disease. We really don't need much, a quantity about the size of a deck of playing cards. Please take time to read The China Study by T Colin Campbell and explore www.pcrm.org and www.strongbones.org.
Because you are breastfeeding right now, it is up to you to get the extra nutrients his body needs to make his immune system more efficient. Please understand I am not implying that your diet is poor, rather, some bodies just need more nutrition in order to experience optimal health. And sometimes, eating well is not enough. We need some extra help because we can't possible eat enough to prevent disease. If you are interested in how my family gets extra nutrients in our bodies every day, let me know.
I am taking series of wellness classes taught by a Naturopath who has her PhD in Nutrition. I have a wealth of information that I can share with you, if you would like. It is my passion to help other moms learn how to optimize their family's health. It is vitally important as kids are getting adult type diseases at younger and younger ages. Let me know how I can help.
Good luck. D.