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It's tricky to describe when to use "en" before a profession. As a general rule, we don't do that. If I described what I do for work, I would say "jag är socialarbetare" meaning "I'm a social worker" without the article before the profession.

But there are exceptions, if someone would point at a person in a doctor's coat and ask who that is you could answer "det är en läkare" meaning "that is a doctor". In your text, it sounds like someone is pointing at a lot of characters and commenting "that's a farmer" "that's a doctor" and so on. Depending on what situation you wanted to describe, that could also be correct.

I hope this was clarifying, :) good work!