Do doctors earn merit on a regular basis as a result of their good acts of treating and curing illnesses of their patients? Is their profession an excellent one because of their chance to earn merit?
There are many kinds of Doctors. There are greedy doctors. There are doctors who treat patients at nominal fees, they are saintly. There are Paramedics, they treat at the level of consciousness. There are technological Doctors, they treat using AI and automatic robots. There are uneducated doctors. There are ayurvedic doctors, Allopathic doctors , Muslim doctors , Chinese Doctors.The list of types of Doctors can be as big as the diversity of characters found in the world.
Not all doctors can be called good.
Doctors , patient , diseases , treatment are a result of combination and separation in time and place. For example-Some treatments are only possible in USA. Some treatments are only possible in future. But all combinations and separations are impermanent.
Consider the Dhamma of Doctor: Treat all patients without discrimination.
However this Dhamma can not be Self. Why ? Because the Sankharas of Doctor are impermanent. Form of Doctor is impermanent, Feelings of Doctor are impermanent. Perceptions of Doctor are impermanent. Choices of Doctors are impermanent. Consciousness of Doctors are impermanent.
Therefore it is not a good idea to get attached to the idea of Doctor. In the end the cravings to exist in any form , feeling, perception, choice and consciousness must diminish and eventually end.
As stonux' answer says, it's the intention that's meritorious -- the act of doing good because of that intention, preserves the merit (see The Essence of Merit).
My guess is that when someone says, "I want to become a doctor", the intention is, "because I want to help people", which I think is generous.
Secondly, Merit - A Study Guide talks about developing "a wise sense of self". It seems to me that a doctor has an opportunity to do that -- to see that the body is impermanent, and what it "requires", and so on.
So I think that answer is yes, but also no -- because I'm not sure you could say that "all" doctors earn merit, nor "on a regular basis", nor because of their "acts". It is my experience, though, that many of them seem to be well-intentioned, and I suppose that their profession gives them opportunities for meritorious activity.
Even so I think (I don't want to find the reference) that the suttas say that (monks') giving dhamma is more meritorious than other activities, such as (doctors') giving medical advice.