Since the other ones, probably little Julia´s siblings are working at the factory, they are in the late 18th century and the early 19th century,during the Industrial Revolution.
Little Julia and her family are really poor, and even when there are a lot of rules against child labor, they are immigrants, so they are not considered American and their employers think the law does not cover them. The working conditions are horrible: they are severely punished if they arrive late to work and if this happens, the punishments can cruel, so little Julia probably would not have a lot of time to look after her sister and might be thinking about going to work, specially because they need the little money they would earn.