If you're interested, contact a recruiter now. Find out all you can and determine if, with more information, it is still something you're interested in. Find out if there are things you can do with your education that make you a more attractive candidate. (Why wait until the last minute to find out that they look favorably upon a Military History course that you could easily have taken as an elective in your next semester?) If the particular program you're looking at or Base you are interested in is being closed in the foreseeable future, would you still be interested in the Navy? If it's military service that interests you, explore the Army and the Air Force as well.
Having more information is never a bad thing, and it may help you to plan out your next few years.
This summer, the chances are they will not even contact you until the fall once you start your junior year. Even if you contact them now it will take months before they get back to you. If your school has a nursing job fair go to and see if a recruiter is there. They will be able to grieve you a better time line when to put in papers.