Answer:
Of course, you would need to build some sort of watercraft. The most feasible would be a raft.
However, leaving a deserted island is not necessarily a good idea. It is incredibly dangerous; on the ocean there is no fresh water, unless there is plenty of rain and you can capture it. Second, there is no food unless you have an ability to deep-sea fish on the way. Third, a storm can take out a raft with incredible ease.
Thus, you would only try to leave an island if:
1. You had been there at least a week and no help had arrived;
2. You were very close to another inhabited island or the mainland.
Note that trying to use a raft or other water craft without an oar, sail, or other means of propulsion is almost certainly 'suicidal.'