May I ask which school? (You can private message me). I actually took a similar route: private day school in the Princeton area for K-8, then applied to Lawrenceville as a day student; I am now a sophomore there.
Anyways, I barely knew the school existed (or that you had to take the SSAT, write an application, etc.) until late in my seventh grade year, so if you start preparing this early, you’ll really be ahead of the curve. Good luck!