Rabbi Yehuda Spitz discusses the matter in the Yated Ne'eman and summarizes the three main approaches.
The Shulchan Aruch Oruch Chaim 551:10 states that the person making havdallah should drink the wine. The Gra explqains that this is because havdallah is no worse than a seudas mitzvah, such as at a bris or a siyum. Sefardim follow this psak.
The Rama says that if possible, the kos should be given to a katan. However, if there is no katan available to drink the wine, th person making havdalla is allowed to drink the kos.
The Magain Avraham says that the child must not be old enough to mourn the bais hamikdash, but must be old enough to understand the need to make a bracha on the wine. This avoids the problem of bracha le'vatalah.
So, basically, to fulfill the Rama's ruling lechatchilah, the child must be in the ballpark of 6 to 9 years old8; otherwise, it would be preferable for an adult to drink it. This ruling is followed by most Ashkenazic authorities, including the Magein Avrohom, Chayei Adam, Kitzur Shulchan Aruch and Mishnah Berurah.9
The third option is to replace the wine with beer. The Aruch Hashulchan prefers this option because he considers beer chamar medinah. However, the Magein Avrohom and the Vilna Gaon ruled that in Ashkenaz, beer has lost is status of chamar medina and is therefore not usable for havdalla. The Chazon Ish ruled that even if beer was chamar medina in the time of the Vilna Gaon, it no longer has that status in our day, especially based on how it is viewed in Eretz Yisrael.
Even many of those who would consider beer chamar medina would allow it only when wine is not readily available. Thus, beer would not be used in our day since wine is readily available.