All I can find is she lived from 1801 to 1825.
From Wikimedia.
Caroline wears a straightforward dress with some ornamentation at the neckline and sleeves in this Rothe portrait.
Keywords: Rothe, Caroline Friederike Mathilde von Waldeck-Pyrmont, Waldeck-Pyrmont family, Württemberg family, Duchess, German, curly coiffure, bun, off shoulder bateau neckline, pleated bodice, quarter length puffed sleeves, waist band, natural high waistline, A-line skirt, necklace, earrings