According to her Wikipedia article, she was the only Grand Princess of Russia to marry a Habsburg and become an Archduchess of Austria.
Her father died in 1801 so that date may be more appropriate, if the black signifies mourning dress.
From Tumblr search.
This dress combines the lavish use of lace and exuberantly curly coiffures of the ancien regime and what appears to be the new silhouette.
Keywords: 1800, Alexandra Pavlovna of Russia, Erzherzogin von Österreich, Alexandra Pawlowna Romanowa, Romanov family, Habsburg family, Grand Princess, Archduchess, Hungarian, curly coiffure, bandeau, jeweled ribboned headdress, veil, earrings, necklace, bodice, lace modesty piece, jeweled neckline, lace bertha, close virago sleeves, jeweled arm bands, jeweled skirt ornament, close skirt