then I'd argue that she almost has to include information about Catherine's childhood, since that's the m.o. in the genre she's parodying (is that a word?). But that she does it so briefly, as others have said, is just another of the contrasts that she makes. It also, I think, adds to the sense of Catherine's ordinariness - there are no great traumas that she's had to overcome, no horrific events that have shaped her life... just a normal childhood for an average girl, and that doesn't take too many pages to describe.

I think another clue that she's intentionally shortcutting the traditional gothic detail comes in the last paragraph of Chapter 4:

This brief account of the family is intended to supersede the necessity of a long and minute detail from Mrs. Thorpe herself, of her past adventures and sufferings, which might otherwise be expected to occupy the three or four following chapters; in which the worthlessness of lords and attornies might be set forth, and conversations, which had passed twenty years before, be minutely repeated.