I think starting early will definitely help you. It is highly competitive out there, and showing eagerness is always good. Have you decided what field you want to start with, or are you ok with applying withing any areas. If you lack experience, best thing to do while you are waiting for interview is to volunteer. It ll show that you have initiative and you are not just waiting around, but being proactive towards your search for a nursing position.
You can always get a temporary license if you get a position early:)
I wish you the best of luck.