I was never your sidekick
Unlike DC which makes a habit of bringing young super heroes up as a sidekick to a well-established hero Marvel rarely makes use of the practice. In Marvel comics most young heroes either obtain their own unique title or take over a title for a hero who has moved on from that title. Kate does neither. She joins a team of young heroes and establishes herself under the same name as an already established hero (although it should be noted he was dead at the time) and is able to work alongside that hero not as his sidekick but as his partner.
That isn't to say that Kate Bishop doesn't have things she still needs to learn. Clint Barton has taught her a number of tricks that help her out in the field but she also teaches him how to act like an adult despite the fact that she is far younger. It is because they each bring something different to the table that they work so well as a team, at least whenever they aren't arguing among themselves.
I think this is one of the most impressive things about Kate. While other young heroes, particularly her allies in the Young Avengers, are mostly satisfied with their lot as a junior hero Kate is looking for more. She proves herself to be a leader when she gives the Young Avengers a place to work out of and picks up the slack for the struggling Patriot. She stands up to Captain America and criticizes him for his inaction when it came to young heroes, something that many established heroes wouldn't have the guts to do. She also makes sure Clint recognizes her as an equal and a stable influence who can bail him out when things go to hell. She doesn't let him treat her like a lesser hero just because of his experience. What's more is that she's paved the way for other young heroes to appear outside of tie in events, as serious members of the Marvel universe.