This is my first post, but as a recent DEPer and soon-to-be-shipper, I thought I may be able to offer some insight.
One: Jayhawk gave some great advice, as I've noticed he often does since I've been reading this board. In May (when I finally met weight regs and was able to go to MEPS and ship) my recruiting station had a very difficult time getting people placed in any job other than AECF (Advanced Electronics - Computer Field, I believe) and Nuke. I managed to catch view of a memo on my recruiters desk stating that they were not to do any active recruiting for people other than Nukes or SEALs (not even SWCC, Diver, or any other special warfare ratings). At one time this summer, my DEP group was 9/18 future nukes, because the Navy simply didn't want anyone else. Given that, I would guess that the Navy is always in need of Nukes, no matter how overmanned they say they are.
Two: As far as the ASVAB, and this is probably the most useful information I can offer, is to actually STUDY for it before you go. Take ALL of the practice exams on military.com, etc, and look up any questions that you don't know and LEARN HOW TO DO THEM because I found the military.com practice ASVAB was a fairly close representation. I'm not sure if I missed any questions on the ASVAB (I finished the test thinking I knew how to do every question, and that I answered every one correctly), and I'm positive it's because I took practice ASVABs online and learned how to do the questions like mechanical advantage with block and tackle, etc. If what my recruiter has been telling me is true, it is much easier to get a nuke contract if you've autoqualified instead of having to take the NFQT to qualify.
Three: Along the lines of that memo that I saw on my recruiter's desk, I think the fact that you're a woman will go a long way to help you out, as well. Women were stated as a high priority recruiting target, and I can only imagine if you prequalify nuke and express a sincere desire to actually follow through this time, you will be an irresistible recruit for the Navy.
Four: I'm sure this goes without saying, but be absolutely honest with everyone you talk to. No sense trying to spit a line of BS to the chain of command. If you get caught, you're definitely screwed.
If I stepped out of bounds or anything with my post, please let me know and I'll be sure to edit and research further.
One last note, DO NOT SIGN A CONTRACT FOR ANOTHER RATING IF NUKE IS WHAT YOU WANT! If you want nuke, make it happen! I know there's definitely less qualified people out there, don't let yourself get pressured into signing for another rating under the guise of "maybe you can pick it up later on."
Best of luck!