ALL regular military doctors are commissioned officer with rank of Captain(or O-3 grade) at least, else they must be demoted after their promotion. I heard that some nations are gives O-2 grade for interns, though, but that's still higher for normal officer who must start with O-1.
Although it depends on the various military traditions, but most military traditions are based on our current era, and I don't think that most armed forces are stupid enough to not respect doctors, thus doctors are expected to start their career as the commissioned offficer. Among the humanity only Clans does if I remember correctly, for Clans doctors are not the warrior caste. But even for Clans, scientist caste is on the high echelon among the castes.
Nurses are depend on the curriculum to classified as either NCO or officer. But anyway they are also NCO at least. The reason is same as doctor.
Unless you want something akin to 'civilian personnel' that is civilian but work for the military, they surely shares the same rank structure with rest of your officers. And I don't think that doctors are suit for this and you should take your own military doctor with officer rank. Doctor is essential to the business which always push the personnel to the harm's way so you never make it without one, and is a profession worth enough to earn the commission. Also doctors with military rank have the authority to say no for ridiculous orders given by the other military personnel, which is an another reason why they have the officer rank. You may a master tactician, but your doctor is the better person if you want any medical aid unless you are also a doctor as well(and you will need an another doctor for you are also need to command the rest of your force).
You may outsourcing the medical service if the size of your company is literally as it is or even smaller. But if you have the force with enough size to have a permanent branch of your own medical teams, you need at least one doctor and nurse each with officer rank. You probably needs much more.