Can goth people be happy?

Of course they can. I'm a goth who is, I guess you could say, happy (or at least not unhappy, at least not any more than the average person). I mean, I'm not overly enthusiastic about things but that doesn't mean I'm not usually fairly content. I'm just more subdued about it than a lot of people (and my personality's that way overall - I'm not one to outwardly express excitement or interest in something usually. It tends to be more contained). The girl in your class may be the same way. Maybe she's not always smiling or anything, but that doesn't mean she's unhappy or not content.