You have two questions here.
I see one small hiccup with your grammar. As you have noted the
の is the possessive particle here, it is used correctly.
The hiccup I see is that you are missing the
は particle in this sentence.
は marks the subject of the sentence (among many other uses). The subject of this sentence is
あなたの仕事. Therefore, I would correct your sentence to be:
anata no shigoto wa nan desu ka?
Also, I heard someone say, "Doko no iku ka?" But shouldn't it be "Doko ni iku ka?"
A dictionary search of other words spelled iku made it clear that there is no relevant noun spelled iku. It is always good to check the dictionary for possible duplicate meanings in these cases.
The iku that you want is 行｛い｝く, or
to go (among other meanings).
shouldn't it be "Doko ni iku ka?"
Yes, but I would like to make a point about the use of か here. Using か with plain form verbs can come off as abrupt or patronizing if you are not careful. As a beginner, I suggest that you stick to
...ですか until you gain more experience. Say it like this:
doko ni ikimasu ka?