Is it true that an infants immune system will be stronger if sick now rather than later?

Yes and no: Infection often induces the body to develop an immune response unless it overwhelms the body. However, some viral infections can also render susceptible kids more likely to develop asthma. On the other hand, exposure to multiple non-pathogenic (not disease causing) bacteria in early life reduces the risk in developing allergic diseases. Most important- don't skip the vaccinations recommended.