When the book was first published in 1900, the average age of a girl in the United States was around 12-13 years old when she started working or getting married. So, it's possible that Baum imagined Dorothy to be around this age, but still young enough to be considered a kid. But, let's be real, what's a kid these days, right?
In the 1939 movie adaptation, Judy Garland played Dorothy when she was just 16 years old, but the character herself is supposed to be around 12-13 years old, just like in the book. It's kind of like how Harry Potter is supposed to be 11 years old in the first book, but the actor who played him, Daniel Radcliffe, was a bit older when the movies were filmed.
