Katie Kopycat (sometimes mistaken for Katie Copycat Doll) was a blonde, hard-plastic doll with soft vinyl head and lower arms (they were jointed at the elbow) by Palitoy. She sat at her desk, with her right-hand holding a pen connected to the desk and she would copy whatever the child at the other side of the desk wrote with their pen attached to the other side of the mechanism. Katie's head would move as she wrote (her head and right-arm were connected inside the body).
The desk was usually the first thing to break... often followed by the arms at the elbow joints. Katie Kopycat dolls often come up on e-bay, minus original clothes (which I don't remember) and desk (which sometimes comes up for auction).
Having coveted a friend's Katie Kopycat doll and not having had one of my own, I snapped up a couple I found in charity shops when I was a student in the 80's, which I cleaned up and redressed out of pure sentimentality for them!