There's no mystery here.
The title of A Year Down Yonder is quite straightforward—it refers to the scope of the book. The bulk of the novel takes places during the year that Mary Alice Dowdel spends "down yonder" with her Grandma Dowdel, and all the adventures and scrapes that occur within that year.
The word "yonder" indicates just how far away Grandma Dowdel's house feels from Chicago, even though it's in the same state. The place where Grandma lives is a little old-timey town, and couldn't be more different than the bustling city that Mary Alice is accustomed to.