I went into the DNP program as a BSN. I knew that I liked critical care and OR. I had NO idea what I wanted to do in regard to my clinical inquiry project, and as I started with one area (family centered care), it switched to anxiety in mechanically ventilated patients, to managing ICU psychosis, and finally ended up with enteral nutrition in mechanically ventilated patients (graduating 12/10, yay!) My program was 4 years though, because I only had my BSN, so I had the luxury of changing my topic, with time to work on it. I think most of my class had a more clear cut idea of what they wanted to do though. You do need to be careful about crossing boundaries in the specialty areas (there is a specific degree for psych NPs, and since your education didn't focus on psych, I'm not sure that would have been wise, but I don't really know what FNP education covers, as I am in an ACNP program, so please forgive me if I am wrong). Any way, if you love derm, then you do have an area that you are interested in. Now you have to ask yourself if there is something about derm that you think should be done better, or differently. If you really want to do the DNP, start looking into what research is out there. There is a lot about the DNP that people do not fully understand, but that is sort of beyond this thread.
In terms of helping you find a job, I don't know that it would help you. It is a new degree that people do not know much about, and there is still a lot of unnecessary rhetoric about it. Most of it is based on ignorance about the purpose of the degree and the rigor of the program. I guess that if you want to pursue your DNP, then go for it. But do it because it is something you desire to do, not because of potential job prospects. You will find that most employers will take experience over a degree. With that being said, you now have some experience in your field of choice even if it has been short. If it is taking that much of a toll on you...it's probably not worth it. Sorry that you are so miserable. We spend too much time at work to have it affect your health . Good luck!