traveling with 3 month old

Would you travel to Nantucket, we live in NJ - 5.5 hr car ride and 2 hr boat ride with a 3 month old? Im leaning towards no bc she can't wear sunblock, july is so hot, and I can't really do much at a beach town when I don't want to take her to the beach. Our pediatrician said she really should stay in the house once we get there because of heat and sunblock.