The minhag not to cut the boys hair is intrinsically tied to the mitzvah of payos. Therefore it would not apply to girls.
The Tur notes the words of Chazal "when a male comes to the world peace comes to the world." We celebrate the additional dimension of peace that has come to the world with this child. Indeed, this is why the celebration is called shalom zachar, which is translated as the "peace of the male."
Perhaps another reason. According to Kabbalah, a child is not ready to be circumcised until he has gone through a Shabbos, for the Shabbos provides the infant with the spiritual power necessary to enter into a lasting covenant with Hashem. (This is (one of) the inner reasons why the Brit is on the eight day, to ensure that a Shabbat passes). For this reason we make a special celebration on the Shabbat after the baby is born.