Are you saying that that equation is wrong? Because KellyR is right if we assume that 0.6c is the speed of the ship as observed from outside the ship. The thing you're talking about is length contraction, not time dilation, although the two are related. To an observer on the ship, the distance to their destination will actually be shorter than to an outside observer. But, what we're talking about here is what an outside observers sees, because we're the ones looking for the ship.
For completeness the time experienced by someone traveling at a constant 0.6c for say 1000 years is t'=t*sqrt(1-v2/c2) where t' is the time observed in the ship and t is the time observed by us. So according to the clock on the ship 800 years have passed while 1000 years have passed for us. Similarly while we would see the ship travel 600 light years in 1000 years times, that distance would actually appear to be shorter to an observer on the ship by a factor of 80%, so 480 light years. In addition to an outside observer, the ship itself would appear to be contracted parallel to its direction of travel. And if we could actually look in the window of the ship everything would appear to be moving at four-fifths speed, while to the people in the ship looking out we'd appear to be sped up.
Sorry, special relativity was one of my favs in undergrad.
