The Shulchan Aruch (OC 551:10) says you may drink wine for Havdalah during the nine days, while the Rema says we are machmir and give it to a child. The child who drinks the wine of Havdalah, says the Mishan Brura, must be over the age of Chinuch for the mitzva of Havdalah and below the age of Chinuch for aveilus of Yerushalayim. This would be between the ages of 6 and 9 according to the Chavos Ya’ir in Mekor Chaim or 10 according to the Mei’am Lo’eiz. The Steipler Gaon, Rav Yisroel Yaakov Kanievsky used to give wine to a Katan until the age of Bar Mitzva.
If there is no boy, points out Rav Elyashiv, do not give it to a girl. Most poskim hold if there is no child it is preferable to drink the wine yourself rather than make on beer.
Rav Shlomo Zalman Auerbach drank the wine himself even if there was a qualifying child available, since halachically it is not really a problem and the exact age of chinuch for havdalah and aveilus is not very clear. Revach.