In Avatar: The Last Airbender because of the possibility of war with the Fire Nation Aang was told about his status as the Avatar at the age of 12, 4 years earlier than the traditional age of 16 by revealing the connection between his choice of the 4 toys he selected as a child. Obviously this means at Age 16 an Avatar begin their formal training to master the other 3 elements.
In Avatar: The Legend of Korra the Order of the White Lotus discovered the next Avatar after the death of Aang in the Southern Water Tribe but unlike Aang the discovery wasn't made by the selection of 4 toys, rather Korra, being a pot-belly a 4 Year old water bender demonstrating not only Water Bending but Earth and Fire Bending.
Sure she may haven't mastered Water, Earth or Fire bending but Aang was only Air Bending up until he was 12 (+100 years of him being frozen) until he began to travel with Katara and Sokka. Does this make Korra a prodigy as an Avatar being able to bend other elements at 4 years old?