Dryad is not immortal, but she can live longer than dragons. but only a few of them consume the maximum of their lifespan. Some say Dryad dies once they try to covet something material, and the other reason is because Dryad knows their death upon birth.
At birth, the Dryad will see a glimpse of their death before actually seeing the world they will live in. The world tree called it a perk because dryads have the chance to avoid their deaths because of the forewarning, but some dryads unofficially call it a curse because knowing your death will make you keep thinking about it, worry about it, and not have a proper view of their current life because of the fear of death.
This is also the reason why Dryad serves the world tree closely, because the more they follow the world tree order properly, the better the chances are that they will be safe to meet the prediction they saw in their birth.