I have this in my files as dating from 1806. However, the dress dates this to maybe a decade later. She was regent in 1814-1815. Her Wikipedia article is here.
Fashion elements of later style, stiff material, a lower waistline, an A-line skirt, and rouleaux, are parts of the dress worn by Queen Marie Sophie.
Keywords: Eckersberg, Princess, Queen, Hesse family, Oldenburg family, Danish, curly coiffure, feathered cap, veil, bateau neckline, bertha, quarter length puffed sleeves, engageantes, waist band, Empire low waistline, A-line skirt, maxi-skirt, rouleaux, necklace, earrings, gloves, fan