Could a penal colony in those islands have been created, or is it so hard to live there that no significant numbers of people could be supported.
Why would you need or want to build ships?
Because the seas are boiling with food. You can support some people on potatoes, rhubarb, etc, but not a lot. Berries, bird eggs, penguins, etc add a bit.
But if you can harvest the seas, you can suport a far larger population base. The problem is, if you cannot replace your own ships, you are extremely vulnerable, with a population much bigger than what the islands themselves can support.
The Falklands are too small for all the British prisoners, the islands would be full very soon. Or did you have a special sort of prisoners in mind?
The Falklands are larger than most people think. They have approximately the same land area as Northern Ireland, for example.