How far does diplomatic immunity go?Watch
Under the VCDR 1961, those who enjoy full diplomatic immunity, a category which includes ambassadors and secretaries in foreign embassies, are exempt from all prosecutions in the countries within which they are residing, or at least those who are party to the Convention. Thus, in the above case, I think the doctor would be exempt from prosecution entirely. Lower-ranking officials, however, only enjoy functional immunity meaning they can be prosecuted if they are acting outside their duties as a diplomat. If the doctor was found to be in such a category, it follows that he could typically be tried and potentially convicted.
It would be likely, in the above circumstances, that the home country would waive his immunity due to the severity of the crime of which is he being accused coupled with the fact that he was wholly working outside of his duties when the incident occurred. As is understandable, there has been a lot of criticism, but it has always been agreed that a country would treat diplomatic officials as it would like theirs to be treated if the scenario were reversed.