I need help with a postgraduate essay. I want to compare two novels from the Gothic era, Wuthering Heights by Emily Bronte and The Brownie of...

The first thing you will need to do to create work on the postgraduate level is to sort out some factual details.

The Gothic period was the late eighteenth century. Wuthering Heights, although borrowing some of the literary conventions of the Gothic, was written in 1845, considerably later than the classic works of Gothic fiction such as The Castle of Otranto or The Mysteries of Udolpho. The Brownie of Bodsbeck (1818) is somewhat closer to the traditional Gothic in period, and in its historical Scottish setting resembles The Bride of Lammermoor (1819), blending a Gothic atmosphere with Scottish regionalism. Thus one issue you need to mention is the 27 years between the composition of the two novels and the difference in situations of the authors (Hogg was a Scottish man, Brontë an English woman).

Next, you should note that Katherine is not, in fact, "horrible" nor is she actually possessed by an evil spirit. The "Brownie" turns out to be John Brown, a man fighting for religious freedom. As for Catherine Earnshaw, she is an ambivalent character, but one should note that as Heathcliff is violent, vindictive, cruel, prone to unpredictable emotional outbursts, and abusive, Linton would be a far more sensible choice for far more than just monetary reasons; he would also be a better father as Heathcliff engages in what we now would consider child abuse.

Both novels have a wide range of female characters. Interestingly, the characters portrayed as having the most knowledge, and often holding information unknown to the protagonists are female domestic servants, Nanny in Hogg's novel and Nelly Dean in Wuthering Heights. This suggests an interesting way to organize a paper by thinking about how class and gender intersect. In both cases, lower class women bear some form of true knowledge and sustain local traditions and memories, often almost subversively, keeping secrets from the upper classes and men, and having a power rooted in observation and empathy. 

For a postgraduate paper, you want to avoid such terms as "horrible" and attempts to judge literary characters as though they are actual people. Instead, you want to think about the construction of female characters in the novels as reflecting historical or ideological contexts. You might look at how the women of The Brownie of Bodsbeck operate within traditional feminized spaces, and end up achieving the closure of happy endings in their role as nurturing and supportive, while the women of Wuthering Heights are far more conflicted in their roles. 

In writing an essay, you might want to narrow your focus. You could look at the difference between Hogg's concern with nationalism and religion and Brontë's purely psychological fiction or think about what the two authors consider the ideal of womanhood for women of different classes. Another possibility would be to look at the language used to describe women in both novels or the way the viewpoints and narrators affect how we see the women of the novels.