The only way for our bodies to build immunities is to be exposed to germs. That's probably why your 18 month old is sick all the time - exposure to different things than his body is accustomed to.
That being said, our son was 2 when we put him into day care from in-home day care. Our daughter was 9 weeks old. He was barely sick and still isn't. 1 ear infection to date, and he's almost 4. Our daughter, on the other hand, has had 10 ear infections in 2 years (5 since getting tubes a year ago).
Different kids have different immunities.
Here's a hard lesson I learned when my kids were much younger. The day before my son's second birthday and a few days before my daughter turned 11 weeks old, I was diagnosed with cancer. 5 months of chemo basically knocked-out my immune system. I had no white cells for most of the time, and I had to be careful that my kids would give me an infection I couldn't fight. Plus, I worked the whole time going in and out of doctor's offices with sick people as a pharmaceutical representative.
One of the Oncologists I saw gave me this advice when I asked if I should take a leave of absence to protect against germs: "Have you ever heard of washing your hands? Then do it often".
I was only able to nurse my daughter for 3 months because of chemo. My son got the full year. Our pediatrician doesn't believe her being prone to ear infections has anything to do with the 9 month difference in breast milk availability.
I'd just advise having lots of hand sanitizer around. But, I'd also recommend having your older child in day care at least part time while you recover and bond with your new baby. I didn't, and I really wish I had. My kids were 21 months apart, and the older was still so needy which prevented me from focusing on my daughter as much as I wanted.