WI: Independent Falklands?

Suddenly had a weird idea while I was reading about the Falklands War on Wikipedia. What if oil was discovered and exploited around the Falklands early, causing a population boom as workers come from Argentina and other places to find work? (This requires the actual technology to exploit underwater reserves, of course, but we'll talk about that later) Could we see an independent Falklands?

For that matter, could we ever see an indepedent Falklands?

The problem with an independent Falklands is that is removes a lot of the motivation of the UK to defend it, while doing nothing about Argentina's claims on the islands. Suddenly they are a tiny, geographically isolated state, with a giant neighbour with designs on conquest. East Timor, anyone?

As for the population boom, it would depend on when the oil was discovered. Post-War, you can forget about workers from Argentina, they would be viewed (ironically) as colonists; it was only a few years ago that tourists from Argentina began to be allowed to the islands, and the first load were met with protests IIRC.

I can't see it happening pre-1900, and yes I agree that the biggest problem with declaring independence is that it from that point onwards becomes easy pickings for Argentina with no real reason for Britain to defend it.