Is Emma a coming-of-age novel?
The typical coming-of-age novel tends to focus on a person even younger than Miss Emma Woodhouse. She is only twenty-one, which is certainly plenty youthful, but she is not exactly a child in the world. Most novels that can be described as having a protagonist that comes of age deal with children who readers watch grow into adulthood, or at least young adulthood. In this respect, one might not refer to this text in this way.
On the other hand, Emma is very childish initially, and she does mature a great deal during the course of the book. She gains a sense of her responsibility as a woman of means who is respected in the community. She learns that kindness and charity are more important than gossip; she also learns to be less officious and to stop meddling in others' affairs. In this way that she grows up, then, you could call the book a coming-of-age novel.