After your baby has reached the child level and has 60,000 FP or more, the Harvest Goddess will visit your house and take you to her spring, where she'll give your child a piece of grow-up Candy. This special treat will transform your child into a teenager for 30 days (not a full 31-day season). There is another random event that you can trigger when your baby is a teenager, but it requires you to have seen the random event from when it was a child.
When the grow-up Candy wears off, the little one will return to its cute child stage. If you want another piece of Candy, give Alice the Harvest Sprite some Royal Jelly. You can get Royal Jelly from your production honey bees. If you seed a bee hive with a Mountain Honey Bee from the Ancient Ruins, then you'll get the honey you need for more Candy.
A teenager's schedule is a little different than the child's. The teenager won't go to bed until midnight, and its Random B locations are the farmhouse and the mine, instead of the farmhouse and the mountain.
Even as a teenager, the child won't help you with any farm chores. Just like with your spouse though, you can ask it to forage for wild items on Fridays or Saturdays, but only if they have 30,000 FP or more and the weather is sunny. Once the teen converts back to a child, it won't help with foraging unless you feed it Candy to return it to teen-dom.