Time dilation! Time is relative. For an outside observer, over 1000 years pass, but aboard the ship, much less time passes. There are calculators for this, e.g. at [0]. If you constantly accelerate at 1g, flip around at the halfway point and accelerate in the opposite direction for the rest of the journey, roughly 13 years would pass from the traveler's perspective.
This site also has a "Newton's universe" mode, which pretends that relativity doesn't exist. Interestingly, in that case you would take over 44 years!
I am pretty rusty in special relativity, but IIRC, in the ship it basically seems like the distance is contracting as you accelerate. And from earth, it seems like time is going slower inside the moving spaceship.
With relativistic time dilation. 1000 years will pass on Earth, but on tge ship, it will be only a couple of decades, assuming they're close enough to the speed of light.