The Ferrari is Bella's "after" car in Breaking Dawn. It is a present from Edward to replace her Mercedes Guardian. The Guardian was a loaned car and it was returned after Bella and Edward’s wedding. Edward had already acquired the Ferrari before the wedding and kept it hidden under sheets in the Cullen's garage.
After Bella was changed, on the day of her 19th birthday, Edward and Alice argue over which present Bella will 'open' first. Alice wins the argument and shows her the cottage.
Edward concedes partly because Jacob is sleeping at the time. Edward anticipates Bella's lack of excitement for the car and remarks "It's probably better that I wait for morning, anyway" so that Jacob is awake and "that someone there is able to express the right level of enthusiasm."
In the novel, Edward allows traditional vampires to borrow their cars and go out of state to hunt, and is therefore described as a gracious host. This compromise made Bella somewhat uncomfortable; however she notes that the other vampires would all be hunting somewhere in the world, regardless.
The model of the Ferrari is never mentioned in the book.