Best way to respond to a request for CV after graduation
Just send a note with 1 to 3 short paragraphs.  


Remind her of the work you did together (you are colleagues, brothers in arms).  
Give her an update on what you have done during the last 6 months (e.g. papers you published, your thesis, courses you took).
Let her know what job options you are looking at (even prospects). Ask her for any advice on your prospects and whether she knows of any opportunity at her place or elsewhere.
Thank her for the time together and how it benefited you.


And yes, include the CV.