Where did John the Baptist get the authority to baptize?

According to D&C 84: 23-28 (http://scriptures.lds.org/en/dc/84), after
the Melchizdek Priesthood was taken from the earth with Moses, the
Aaronic Priesthood remained, even up to the time of John the Baptist.
His father held the priesthood and as the oldest son of Zacharias John
would also receive it. Joseph Smith said: "The Levitical Priesthood
is forever hereditary – fixed on the head of Aaron and his sons
forever, and was in active operation down to Zacharias the father of
John" (TPJS, p. 319).

John was filled with the Holy Ghost from his womb (v.27). When Mary
who was carrying the unborn Savior visited Elizabeth, John leapt in
her womb.
John was baptized as a child (v. 28) and ordained by an angel at eight
days old to become an Elias, the forerunner to the Savior.

Although Zacharias was killed by Herod's soldiers, before his death he
must have baptized his son and ordained his son to the Aaronic
priesthood. Zacharias and Elizabeth were likely witnesses to their
son's ordination by an Angel of God to the calling of Elias. It may
have been about the same time that he was circumcised, received his
name and a blessing from his father (Luke 1:59).