I'm not sure there's a way to find out, given that it seems dragons seem to get murdered before they live to old age. At least from the sound of the protagonists predecessors. The huntress herself has said she's killed numerous ones.
I'd question if they are immortal otherwise though. Since there's no male elves, wouldn't that mean they have a limited dwindling population? They'd have to live a loooong time to just stave off extinction.