Cool headed girl with quality (5)
I believe the answer is:
class
This clue could be a double definition.
'cool headed girl' is the first definition.
'class' can be an answer for 'girl' (I've seen this in other clues). I'm not certain of the 'cool headed' bit.
'quality' is the second definition.
(class is a kind of quality)
'with' acts as a link.
Can you help me to learn more?
(Other definitions for class that I've seen before include "Set, category" , "Order - quality" , "Category; form" , "Category; lesson" , "pupils?" .)