What profession does John plan to have in "By the Waters of Babylon"?
John is the son of a priest: "'I am a priest and the son of a priest!'" In their society, a child doesn't "plan" on having a "profession" in the way that we, in our society, are familiar with. The question pertaining to John's education, work and future calling might be better expressed in terms coherent to his society as: What future work or calling does John envision himself as having? The answer would be: He envisions himself as being a priest as his father is a priest.
John's future work is aptly expressed as an envisioned calling because, as in much dystopian literature, elders select the work children will pursue as their adult occupations. In a sense, John's future work might be called a "profession" since it will require years of specialized education, training, practice and initiation. In another sense, the sense pertaining to their specific social developmental time--which is different from the dystonian chronological time that includes the pre-Great Burning era (i.e., equivalent to our time)--John's society is so backward that the comparative development of their society predates the comparative introduction of the word "profession" into their total chronology. To clarify, the word "profession"--in the sense of work done that requires extensive education and training and intensive practice and initiation (in our times, initiation by way of licensing exams as for a license to practice medicine or a license to practice law)--was introduced in 1610, while John's society is depicted as having reverted to a prehistoric period, especially evident through the depiction of the "Forest People": "We are not ignorant like the Forest People—our women spin wool on the wheel, ... [w]e do not eat grubs from the trees,...."
We are told that John's elder brothers are hunters: they are brave and respected because they are the elder sons of a priest. We are also told, though, that they are not brave enough to venture to undergo the test required to follow in their father's steps and become priests: If they were to take the test and fail, they would die by being "blasted": [John says,] "I took [the metal] and did not die. ... [M]y brothers would not have done it...." In John's society, a boy may dream of a future position but may not be permitted to fulfill the dream by his own plan alone, as may have been the case with John's brothers (one may have dreamed of being a priest but fear of the metal-holding test prevented him from trying to fulfill his dream). In contrast, a boy may be encouraged to aspire to a future work because he and his father both dream of it, as was the case with John. In John's case, his father was a respected priest, and he wanted John, his third son, to be a priest, and John, in return, dreamed of being a priest like his father.
Then my father came out with the metal—good, strong piece. He looked at me with both eyes but I had not run away. He gave me the metal to hold—I took it and did not die.
In terms coherent to John's society: John dreamed of being a priest; he undertook the test to be a priest; and he past the test to be a priest: "[I] did not die." Consequently, upon passing the test, John expects to undergo the education and training required, which his father will administer, and to succeed in his initiation, "I came to my father and said, 'It is time for me to go on my journey. Give me your leave.'"
As to John's plan for a profession, since John's training to be a priest begins as a matter of course after his metal-holding test, since it begins as a matter of an automatic series of events that occur to him beginning with being fed and treated differently ("they gave me the good piece of meat and the warm corner of the fire"), and since these events occur under his father's watchful eye ("My father watched over me—he was glad that I should be a priest"), it is incorrect--it is anachronistic (of the wrong date)--to speak of his "plan" for a "profession." Notwithstanding, we can very clearly say that, based on the protocols, traditions and rituals of his society, John has been selected to be a priest and that he is glad, because being a priest--like his father is a priest--is John's dream. As the fulfillment of the tests, requirements and desires of his society, John is inducted into plans for being a priest that require fulfilling his education and training and passing his initiation ("I asked for and received purification. My body hurt but my spirit was a cool stone") and succeeding in his quest ("Now go on your journey"): "[H]e said, 'It is forbidden to travel east.' ... Then I knew I was meant to go east—I knew that was my journey."
My father is a priest; I am the son of a priest....
I was truly his son and would be a priest in my time....
"It is time for me to go on my journey. Give me your leave." ....
[He said,] "This is a strong dream." ....
"It is mine," I said,....
John is chosen to be a priest, so he plans on being a priest. John is the son of a priest, so he begins his life with the welcome expectation that he might be able to become a priest someday.
My father is a priest; I am the son of a priest.
What's interesting about the society that John lives in is that it is not guaranteed that John, or any son of a priest, will become a priest. John has brothers, but neither of them have been chosen to be priests.
The following quote is from when John is taken to the "Dead Places," with "bones in the shadow," where he is given the metal-holding test for the priesthood: "[Father] gave me the metal to hold -- I took it and did not die." The quote goes on to explain that his brothers, although brave hunters, would not have had the courage to take the metal-holding test: if they failed it, they would fail by dying. The brothers will not be future priests.
my brothers would not have done it, though they are good hunters.
The test that John had to pass has two parts. He was to go to a Dead Place with his father and not run away. That was part one of the test. Part two required John to grab hold of the piece of metal that John's father held out to him and not die.
Then my father came out with the metal—good, strong piece. He looked at me with both eyes but I had not run away.
Once it is determined that John will be a priest, he begins to receive special training. He learns to read and was always given the best spot by the fire and the best food. He was punished more severely if he "boasted or wept without a reason" and is held to a higher standard than other members of the community.
The short answer to your question is this: John is planning to become a priest.
In this story, John is the main character. He is the one who, as an adult, violates the law and goes across the river and sees the "Place of the Gods." The reason he does this has to do with what profession he planned to enter. As a boy, he goes with his father to the Dead Place as part of a quest--it's his journey of discovery.
He wants to undertake this journey as a boy with his father because it leads to the test in the process for becoming a priest in their society. If John passes the test, he will go on to train for and be initiated as a priest, like his father. If he fails the metal test--his father will present him with a special piece of metal to hold--if he fails, his failure will show in instant death. John's older brothers have not had the courage to take the test. Instead of priests, they are brave hunters.