The note can be found at Cranberry Island Bog. It is the footlocker on a shelf next to the green container in the Eliza family bunker, a hidden room below the house with the parasols. The bunker is in the vicinity of Cranberry Island Bog, located inside a green shipment container, below the house with a chemistry station. However, the bunker can only be accessed by repairing and activating 3 generators throughout Cranberry Island according to Eliza's map of home.
Remember to move all of the supplies from the shed on the East Dock to the storage room here in the bunker. Aside from the generators being in full working order those supplies are our most important asset. And don't make your brother do it! This is YOUR job!
The key is in the footlocker, near the bunker entrance.
While the note says the supplies are located on the East Dock, the supplies are actually located southeast in the Cranberry Island supply shed.