why does she feel dammed and why is she willing to live with that damnation?

The society of this novella is one in which people must never be thought of as individuals. The Golden One realizes that if she joins Equality in his quest to think of himself as an individual and eventually go off into the Uncharted Forest, he will in fact be damned by the World Council. Because the two (Liberty and Equality) have personal feelings for each other and because they begin to think of themselves and each other as individuals, they will have to be together since the society would never let them return.