IMO, if she's a terrible driver then no should be the answer. Some of you guys need to realise that the op is only 22/23. His gf is just as young with no experience of driving anything that powerful. Irrespective if its a Nissan 350 z or a Ferrari, 300 odd bhp is a lot for some. Imagine if she hurt the car with her inside it and also hurt herself.
I let my ex drive my old car, but only as I felt she was a good driver. Had she been not then i wouldn't have. Only person, apart from my brother, who I've ever allowed to drive any of my cars.