A doctor and indeed many other healthcare workers can pronounce life extinct. ie the patient has died. The doctor should make a written record of it with the time etc.
What then happens depends upon where the death occurred. If it occurred in the UK the doctor can write a death certificate if he has enough knowledge to be certain of causation, if there is no foul play and certain other issues have not arisen such as an operation within the immediate past. Otherwise he has to inform the coroner. In practice if the death occurred in hospital or at home we speak to the coroner's officer, often a retired policeman, and he then agrees or otherwise that we can sign the death certificate. If not then the body goes to the coroner for post mortem and he signs the death certificate with or without an inquest
Where a death is sudden or unexpected or outside the home eg in an aircraft then it is highly unlikely the doctor has the necessary information to inform the coroner so the body would be collected and taken to a mortuary who would then inform the coroner
Theoretically the aircraft's registration determines its territory but in practice the authorities at landing tend to handle it unless the body has diplomatic or political immunity, and then every country has its own rules.