If a meteor was going to crash into the Earth and completely destroy it, would we have an evacuation plan? Would they try to ship us all to the Moon?

No. We have precisely zero ability to evacuate this planet.

Should an asteroid large enough to destroy Earth end up on a collision course with us at any time in the near future, the human race would quite simply be doomed. There is literally nothing we could do against such a threat. Our technology is not anywhere near being up to the challenge, and isn’t likely to get there in our lifetimes. (As an aside, a rock big enough to have this effect is called an asteroid. Meteors are smaller.)

Given a lot of warning, we might potentially be able to divert an incoming asteroid. We would have to send a bunch of missions up, over a period of decades, to detonate explosives on the right part of the asteroid to slowly change its orbit.

With our current technology we could probably pull that off but, like I said, we would need to know about the threat decades in advance.

As for evacuation? No way.

We could potentially get a handful of people into orbit. With a phenomenal effort we might even get a hundred or so people to the moon. Unfortunately, we couldn’t keep them alive for very long. They would just get to die slower than the rest of us.