While watching the first season finale last week, I was wondering if I had heard incorrectly that she was in the second season. It seemed like the episode was written to get rid of her, but with Eccleston leaving they needed some continuity to bridge to the next season and so left her on (probably not correct, but that's how it seemed to me).
I liked her character overall, but several times in the first season I felt like she was the star and the Doctor was a supporting character. Maybe that will be better with the next one.