Use exuberance to describe joyful enthusiasm and liveliness. You appreciate the natural exuberance of small children, but you prefer to enjoy it from a distance.
The noun exuberance comes from the adjective exuberant, which itself came from a Latin word that originally described an overflowing supply of milk from the udder of a cow or goat! The word still means "overflowing," not with milk but with joy and enthusiasm. After your winning home run, the fans ran onto the field and, in their exuberance, carried you off on their shoulders . . . before you touched home plate.