That doctor might've been the last person alive.
Which doesn't make sense either. When people started getting sick and turning into powder, you would think the doctor would have been the first one notified, so therefore he should have been one of the earliest ones infected and die before the others.
Unless he was hiding in a closet somewhere and only came out after everyone else died.
He would have been one of many doctors on board. Like McCoy, he could've been hanging around the bridge when the outbreak swept the ship. If the symptoms came on suddenly and death by crystallization occurred after a few minutes I doubt there would be any cohesive response to it. The doctor might've thought he had time to send a distress signal after making a quick log entry and miscalculated the timing. IMHO.