The university where I work recently included Gender Identity in their non-discrimination policy. I am not out at work yet, but it starts Monday by meeting with the head of the Diversity office. After that person gets the ball rolling for me, I think my next steps are the Equal Employment Opportunity office, followed by HR, followed by coming out to my boss and co-workers.
See if your school has similar offices. Also, see if your school has a LGBT group and contact them to see if they know where you should start. I got the path to follow from a combination of talking to a another trans employee that has been through it, and from my therapist making phone calls on my behalf.
In your case, I think the sooner you get all your paperwork done to match your driver's license and get that SSN changed to match, the better.
-Jay