Boy, that's a tough one; I surely would not want to wait around until 11:35 p.m.; but everything would have to run like clockwork to get you on the 10:35 a.m. flight. You could probably do it if you purchased the luggage valet option, where they print out your boarding pass on the ship and pick up your luggage right at your cabin and take it to the plane. But you would need to verify with Princess that they have that arrangement with your airline--not all airlines participate in the program.
Otherwise I think I would just check into a hotel near the airport and take it easy for the day. You might even be able to pick up a sightseeing tour at the hotel if you are interested.
Either way, have a great cruise. I'm taking Golden Princess to Hawaii this October and did it three years ago on Island Princess; it is a wonderful cruise.