Kilgharrah is not longer the last of his kind after Aithusa, a white dragon, is born in this episode.
Dragon eggs can live for more than 1,000 years. The eggs don't hatch until young dragons are called into the world by the Dragonlords, who are the only ones who have the power to summon them from the egg. To do that, they need to give them a name. Merlin calls the young dragon 'Aithusa', which in dragon tongue means 'light of the sun'.