I have seen various dates for this, but batguano lists the date as 1795. According to batguano, it was commissioned by Catherine II.
This portrait is a full view of Elizabeth wearing the dress she wears for her 1793(?) portrait showing the dress probably had some mechanical support.
Keywords: 1795, Elizabeth Alexeievna, Princess, Tsaritsa, Baden family, Romanov family, Russian, long curly coiffure, floral jeweled headdress, scoop neckline, modesty piece, elbow length tight sleeves, engageantes, lace, panniers, over-dress, vee waistline, full skirt, under-skirt, order sash, order star, necklace, earrings, bracelets, shoes