No - you only get points for the flights that you take.
However, they could earn points on QFF and transfer them to you.
Some people will suggest that for purely domestic itineraries you could book the flights under your name and she could fly as you. There are few if any ID checks on domestic Itins - especially if you have no luggage and use online check in. That would be unethical and possibly fraudulent.
EDIT
Noticed she is travelling with you so the name game wont work
