Well, that depends...
If your father has money, you might spend your day entertaining visitors to your home by playing the piano and singing. If there are no visitors, you might want to sew something. Why not read, practice your handwriting skills or embroider something? Why not practice your piano playing?
In the evening you can go out to a gathering of friends or to a party. If you are not yet married, you might want to get together with your single friends in one of their homes, just like today.
Do you want to go to school?
If you want to go to college, forget it...unless you want to take up music and your family can afford one of the very few private, church-run music schools.
Because there is a shortage of teachers, you can always be a teacher...but just until you marry, of course. You can't possibly be a teacher in the mid-1800s once you are married. It isn't allowed.
Are you poor?
You should find a position as a servant, commonly called a domestic.
** Get those baths ready by hauling pails of water from the water pump. Oops, don't forget to heat it first in pots on the wood burning stove.
** Empty those bedpans (hold your nose).
** Wash the clothes and beddings. Hang them to dry.
** Shop for the family (no, not for designer clothes).
** Mend everything in the entire house that needs mending.
** Find those dust balls.
** Clean those floors.
** Oh. Don't forget to prepare the meals.
You will be a domestic until you marry when you are around 23 years of age. And once you marry, your place is in the home taking care of your husband (he rules the roost, by the way) and your children. If you don't marry, you will be called a spinster and will probably be a domestic for a long time. And now you know.