Can it be "this job is special" too? Or will that be phrased differently
You can say mijn werk = my job, but it doesn't really work here I think, using werk for job works best with [somebody's] job.
- This job is special. = Deze baan is speciaal.
"job" has two meanings in English - a person's job, or a job of work.
When you say "this job is special" - it has two possible meanings. Either the profession, such as a teacher, or a piece of work that a person has to do e.g. painting a specific house, or doing a specific piece of work for one of many clients. The second meaning is more likely in that particular sentence, and that would surely be better translated as "werk" rather than "baan", unless there's another word for that (like "Auftrag" in German).
You're right, in that sense job works fine in this sentence indeed. And I need to correct myself werk meaning profession works just fine here.
For "profession" you can use werk or baan. In the sense of "a piece of work", you can use werk, or opdracht (that's the direct translation of Auftrag). A third meaning for werk in Dutch is "piece of art".
However in Dutch the more natural meanings are other way around. Either baan (profession) or "piece of art" are the more natural meanings of this sentence. "A piece of work" isn't wrong, but it would need a more specific context for people to think about this meaning. So not an issue in everyday speech or writing, where there's always context.