I've heard it used to mean "to prove yourself".

The phrase originated from criminal world and as far as I remember it was first used in the novel called "godfather" but the language has evolved much from that day, so it can be used for other actions too, like for example, success in something or achievement. In your case she is probably saying that she needs to establish, achieve or want to gain respect as a writer. Hope it helps ;))))

The references I've found say it's a translation of the Italian "devo farmi le ossa". I'd love an Italian speaker to explain their understanding of the phrase, as I'm slightly suspicious that some meaning gets lost in translation when a phrase gets switched so flippantly ("traduttore, traditore"). Anyway, I understand the phrase as meaning that the person needs to create a stable structure or foundation on which they can grow and develop (like dem bones!).

For a criminal, it means to establish one's credibility by killing someone.