Is a world with no protium, only deuterium (and the unavaoidable contamination of a tiny trace of tritium), hence all the water is "heavy water" possible? Sure it is.
All that's needed to be plausible is a plausible mechanism to concentrate the heavier isotope, probably in multiple stages (like multi-step distillation to reduce impurities further and further).
A potential mechanism might be a naturally occuring mass spectrometer, perhaps in orbit of a neutron star. Gas ionized by x-rays and UV, orbiting through the star's hyper-strong magnetic field, will tend to separate into streams of heavier and less heavy atoms. A few million years of this might plausibly separate the gas enough that some later event that strips it away from the neutron star and makes it available for star and planet formation preferentially grabs the denser deuterium.
Now, whether a star capable of sustaining life on a planet can form from deuterium only is a separate question -- at the very least, it wouldn't be where its mass says it should be on a Hertzsprung-Russel chart.
As noted in comments, this may not be a mechanism that can produce enough mass to form an entire star, but might well do to form a rogue planet that can later be captured. After capture, there's still the possibility of surface contamination by comet bombardment, but that's generally an event from early in stellar system formation, where rogue capture might well occur after primary accretion is well over with.