As I speculate, this animal can have model of a reddeer with a different texture on it, can appear extremely rare (1 silver for 1000 regular ones perhaps?), have superior speed and strength, generally be able to escape easily from a single hunter.
As for the loot, the main thing is its superior hide, probably with a recipe for unique clothing.
The White Stag has a message for you. Hunters of old pursued the miraculous stag, not because they expected to kill it, but because it led them in the joy of the chase to new and fresh adventures, and so to capture happiness. You may look on the White Stag as the true spirit of Scouting, springing forward and upward, ever leading you onward to leap over difficulties, to face new adventures in your active pursuit of the higher aims of Scouting.
— Baden-Powell's farewell speech to the Scouts, taken from https://en.wikipedia.org/wiki/White_stag
