This question really depends on what you mean by 'independence'.
Literal independence comes for Jane when she is able to escape her step mother by applying to be a nanny. She is able to leave the house she has been tormented in.
A deeper sense of independence may come for Jane later in the book. It is arguable whether Jane is truly independent, or bound by Rochester. You need to analyze the decisions she makes (her reaction to the lady in the attic, her return to the burning house) to determine if she is truly independent.