It's very unusual for a medevac to take place with strict protocols being observed between current and receiving hospitals.
As pilot dude said, they'll generally only fly patients who are stable, otherwise it's only going to have very bad effects.
In the majority of cases there will be three sets of doctors involved. Those currently caring for the patient, those who will care for them back in the receiving hospital and those who will care for the patient during the flight.
If the patient is very ill, then the flight doctor sometimes travels down scheduled to assess the patient in-situ, before attempting to move them.
I'm sure everything will go well with the flight though.