Why is it that someone has to have some weird power or personality quirk for you people to like them? My God, if they're not either clinically depressed or acting like they are constantly on Red Bull, you hate them. What is that? The whole reason that Katara is such a great character is that she is ordinary. No agsty hidden secrets, no obnoxious hyperactivity. She has a good personality, and she actually treats people like people, and she is obviously a strong young women. She is straightforward; what you see is what you get. Heck, we need someone to keep the sanity on the show. That's Katara's job, considering everyone else is legally insane half the time.
The fact that she isn't perfect is also what makes her great. Like her obsessive compulsive behavior towards fortune telling in episode fourteen. Her shortcomings make her seem more real, not painted with weird personality idiosyncrasies necessary to hide the lack of a real personality like Sokka.
Point is, as much of a loner I am here, no, I don't think Katara is annoying in the least.