Sen to Chihiro no Kamikakushi, Tonari no Totoro Recommendations
The protagonists are of similar age, but the plots involve them growing up and dealing with chances in their lives they don't necessarily like. Both Anime are heavy with Japanese cultural references, yet also deal with interacting with spirits from Japanese myth.
Both are Studio Ghibli classics that revolve around a young girl going on a strange and magical adventure.
Both directed by Hayao Miyazaki (Studio Ghibli). Both involve female main characters and both are light hearted and truly amazing.