In general, doctors generally don't fall ill as often as the general public, despite "increased exposure."
The reason for this is so simple, most people simply can't accept the reality.
Doctors, nurses and other such health care workers avoid illnesses by the simple expedient of washing their hands 40 times a day, after each exposure, before eating, after any "body functions" and after contact with each patient.
There is some speculation that such exposures also help to strengthen the immune system. Personally, I believe there may well be some truth to this, having watched/treated children who's parents were hyper-over protective as opposed to parents that knew children get dirty, have scrapes and bruises, etc. etc.
In general, the "precious jewels" who are "protected" from everything are weaker and and less able to fight off the normal ills of childhoood. This also seems to hold for adults.