Mama wa Shougaku 4 Nensei

Natsumi Mizuki is a 4th grader whose parents have gone to London. Her Aunt Izumi comes to live with her. Izumi is an aspiring manga writer who is trying to get her first big break, so she doesn't have time for a baby that appears out of thin air on Natsumi's first night alone. The baby's name is Mirai and her mother is Natsumi, but 15 years older. Somehow, Mirai had traveled back in time. Now the young Natsumi has to raise Mirai while trying to keep her 4th grade life from falling apart and keep Mirai-chan secret from everyone. She has the dubious help of Izumi and some baby-care gadgets from the future.

(Source: Anime News Network)