It's not at the Ohana character breakfast, but I heard you can ask for it and pay extra. Honestly though... the food at the character breakfast was so good, I would just enjoy that -- warm pineapple coconut bread, and cinnamon raisin bread (both were out of this world good), eggs and breakfast meats and potatos, and fresh fruit were very good.
If you can, I'd make a separate trip to Captain Cooks. The Tonga Toast was only about $5 and you can sit outside at a table and enjoy the view of the water and castle while you eat. The tonga toast is yummy and a big portion.. so if you don't have a big appetite, you could probably share an order.