There are doctors well in reach in case of medical emergency. However, as a safety procedure, we recommend you to carry a first-aid kit and your prescribed medications (if any) during the trip. Also, irrespective of whether you are travelling by water or not, it is better to carry medicines for sea sickness.
Here are a few good hospitals in Port Blair:
GB Pant Hospital – Ph. No: 03192 243 653
Maricar Hospital – Ph. No: 03192 233 434
Andaman & Nicobar Islands Institute of Medical Sciences (ANIIMS) – Ph. No: 03192-232605
Also, for ambulance in emergency situations, call 09540161344