Papajohn will no doubt correct me on this, or at least provide accurate figures and a layman's explanation, but time and space don't work like that and as speed increases, distance shrinks and therefore it would actually take considerably less than 600 years. (As in a few days.)
I remember Professor Brian Cox saying that travelling at 99.9999% the speed of light would allow us to get to the the Andromeda Galaxy (3 million light years away) in only 50 years. So by those figures it would mean it would take about 4 days to get to the new planet. (Although if you turned around and came straight back, the earth would be 1200 years older even though you've only travelled for 8 days - I think!)