Thanks everybody. All great things to think about. And I do realize that there is a huge gaping plot hole here, but hey, so do many great stories that are highly revered. But if I must give a justification as to why they couldn't just destroy the missiles, I would say that an enemy agent infiltrated the military and sabotaged their defenses, except for their escape route, which was kept a mega super secret.
As for things like fish and atmosphere, I have decided that the Universe they are taken to do have those that would be sufficient to keeping the people alive. They somehow find themselves on a planet that seems similar to Earth, except with a lot of key differences, but they're definately not floating around in space. They managed to land themselves in the middle of a vast ocean, but due to differences in the way physics works in this Universe, none of their boats can sail across it. Their planes can't even fly. They think there might be other life and civilizations on the planet, but they have no way of finding them.
I've already figured that they wouldn't have satellite connections, so cell phones, GPS, and satellite TV won't work. I don't know how this would affect internet or cable, but I'm assuming that they would be in tact.
As for imported goods, I'm assuming that the people are just going to have to live with what they already had. They might worry about rationing food for a little while, but then they discover that food grows faster there, and much more abundantly, and with hardly any work required. But I don't know what other products would they have to worry about getting know that international trade is gone?
I didn't give much thought about what would happen to the rest of the world. I figure that once my country leaves it, it no longer becomes relevant. They will probably have troubles, but there is no way anything they can do can affect my country now.
Also, I haven't really figured out how the transportation process works. I'm not basing this story on any sort of hard science at all. It's going to be more of a fantasy story, with "technology" acting more like magic, but only enough to advance the plot. So I don't know how much of the country will be moved, if the tectonic plates will be broke or not, or how much energy will be required for such a feat to be accomplished. My major focus will be on how this people react to their new environment, which will be a lot different than what they are used to.