At the speed we can go we can get there in 80,000 years. I think we need to first build a moon size ship that travels slowly but safely. The humans on this ship know they will die on the ship and many many generations will die before this ship ever reaches its destination.I'd volunteer to head for the new planet if they could get us there in a rapid period of time. Gotta get away from this looney Islam somehow.
We harvest the meteor belt to make this moon size ship.
As technology advances we will build faster ship that will eventually pass this ship but it will serve as a rest stop for people traveling faster in smaller ships.
The only waste of time is to do nothing. Humans can live long after this planet is gone and our sun dies. If we don't escape the human race is doomed just like dinosaurs.