I'm not saying that the Doctor was necessarily a father figure to Rose, but it is certainly what she was looking for when she started travelling with him. The quest for such figure is prominent throughout both series' and ends nicely with the fact that Pete actually rescues her from the void.

Well, that's a point of view. It's completely different from my point of view, but... well, there you go.

Is part of Rose's 'damage' that she lost her father at a young age? Of course. But that doesn't mean that she's looking for another. She has a desire to see and know her own father, Peter Alan Tyler, not reinvent him in someone else.