Even if we manage to colonize another world, there's no way we'll be able to scale transportation and settlement fast enough to move enough people off planet to mitigate climate change here.
How we get there might also be the opposite of what you'd expect. Maybe the poorest 6 billion die first, and the remaining rich manage to survive only by drastically ratcheting down their lifestyle. Or maybe world war 3 happens and almost everyone dies, but the small number of survivors are able to pick up the pieces and build something resembling a modern lifestyle.
That said, not all middle class lifestyles need be so carbon intensive. US in particular has the highest GHG per capita because of sprawl and lifestyle choices. As China and India develop (although that might take a while) we have to help encourage them to not copy the US' example but say certain western european countries which use much less GHG per capita that we in the US do.