I don't know about learning Chinese (E4 joke), but Emma must have shown impressive maturity and cleverness in her early teens. She not only becomes mistress of the house at thirteen (!) but Miss Taylor and Emma develop a relationship as equals. the intercourse of the last seven years, the equal footing and perfect unreserve which had soon followed Isabella's marriage on their being left to each other, was yet a dearer, tenderer recollection. Ch. 1

Even Mr. Knightley is impressed with the reading lists she made when she was just fourteen. The list she drew up when only fourteen -- I remember thinking it did her judgment so much credit, that I preserved it some time. Additionally, he says that ever since she was twelve, Emma has been mistress of the house and of you all. Ch. 5