More to explore:
This is a dress dated 1810-1814, Met. This dress is a good example of only the bodice having a lining, which you would not need to have a bodiced petticoat for. You could wear one very similar to the beautiful extant one posted on this board.
Nursing stays after 1810
Corset, stays, ca 1810
The Oregon Regency Society ~ Northwest Chapter: Achieving a proper fit with Regency stays.
Corset, stays, 1810-50
Sprigged cotton dress, with an overall eyelet design and an elaborate scalloped hem border. Charleston Museum
Dress ca. 1810