This picture book has a girl recalling something like ” when i was a girl on the island ….” she would ride her bike, play flashlight tag with her friends, pretend to be a ships capt, ect. Last page shows her grown up with her own daughter on the island on a beach or something.
When I was a little girl my Aunt gave me a picture book titled “Jessie’s Island”, by Sheryl McFarlane. I remember it having a similar plot.