I found only one article about her and it is here.
From historicalportraits.com/Gallery.asp?Page=Item&ItemID=227&Desc=Elizabeth-Campbell-%7C-Sir-Henry-Raeburn-PRSA; spots and linear flaws removed from the darker parts of the image with Photoshop.
This dress and the dress worn by Anne Gibson-Craig are very similar. The waistline of this dress is just a few cm lower.
Keywords: 1806, Raeburn, Elizabeth Campbell, Marchesa di Spineto, Campbell family, curly coiffure, modesty piece, square neckline, Empire bodice, quarter length notched close sleeves, Empire low waistline, close skirt, wrap