It does sound exactly like what you said - she should be exempt as the dependant of a full time registered student. But as a
post-graduate student make sure that you are able to fulfill the council's definition of a student that is exempt.
I'll tell you why. I am here on a work permit. My husband is a full time registered student in Chicago, although he lives here with me as my dependant. He is finishing his dissertation and doing research here as well at British Library, SOAS, etc. Thus he is what you'd call post-graduate over here (grad student in the US).
We applied for a council tax exemption for him due to his being a full time student and (in essence) not being able to work. Our council rejected the application, saying he did not fit their definition of a student, which was something about being registered for X number of hours at a recognized university, blah blah. Basically what they were saying was he could get a job if he wanted to because he wasn't required to be in classes all day.
We appealed it, saying although he was not attending classes for X number of hours, he was still full time registered at a university and could not very well work a job when he was required to do research full time as part of his degree program.
To make a long story short, it worked and we got the exemption!
![Grin ;D](https://www.talk.uk-yankee.com/Smileys/classic/grin.gif)
I was floored - given the British bureacracy's love of following rules to the letter with absolutely no room for bargaining - I couldn't believe they said ok to it!