You can fish with the fishing pole on both islands.
On the 1st island, go to the ocean, ( located right before you get on the ship)climb up on one of the 2 rocks. Cast at different locations, you can find different items, I think...
On the 2nd island, you can fish at the 'ol' fishing hole (couldn't resist, sorry) by climbing upon one of the rocks.
You do not need any bait. Fishing at different times of day will yield different fish.
Hope this helps. Have a great day.