Place workbenches (and also some wall araund them as mobs can destroy them) and then run araund island till you find a spot where you cant build. On that spot place a new workbench and repeat the process till you can build everywhere on island.

If biomes are to close to island, mobs can still come to you so i recomend you raise terrain all araund island 4 times. But if its just sea and 20 squares away from land, then there is no need. (1 square = 1x4 wooden floor)