Will I be able to move decoration from one island to another?

You can move anything that you can store on your storage ship. Just store in the ship, then when you arrive on the new island, open storage, and take out. Things that cannot be moved include the Estate, 3x3 buildings and stationary things, like landmarks. When you reach Sunflower Island, you get one open plot; the rest will need stars and compasses to open just like on Orchid Island. So don't expect a lot of space at once.