One thing I can see right now that's a problem. Putting aside all the possible problems of the libertarians themselves, well, the nation would have to conform to societal laws of other countries to some degree. IE, if they made giant floating meth labs, the US would just declare war, wait, no they wouldn't, we haven't done that since WWII, so they'd... do military action against said country. Hell, even without meth labs or crazy stuff like that, surrounding countries would just go to war with said country for fun.
It's gonna happen, I think. It's bound to. But, I think their big issue will be that. They'll be bothered by others, either because they're being sorta dicks (giant meth labs) or just for fun by other countries. The problem with arming yourself seriously with a small country like that, you'll basically get invaded for being heavily armed and having missiles or fighter jets and the like. People will consider it antisocial to be such a small country with the amount of weaponry needed to adequately defend itself from nations wanting to invade it, and that'll be a catch 22 for them to get invaded. Oh, and nations could just embargo a small island easily, just run 2-3 big ships up to it and you're screwed.
The only way I can foresee the security questions being solved would be forming alliances with other countries that are on land, then you lose independence, though.
So that's what I see is the bigger issue, not so much how nice or not nice a libertarian society would be. In my opinion, a libertarian society is going to have it's ups and downs, just like a socialist, capitalist, leftist, conservative, etc, place will. But, the fact is, all those places exist on this earth because people decided that was what they wanted out of a government. So it'd be the same situation in a libertarian society. Other thing, too, US started out super libertarian...and got to the way things are now. I can't see why these nations wouldn't just eventually follow suit.
Oh well, I'm skeptically supportive of the idea, I do wish to see it pan out in my lifetime, and probably will see it happen.