The thing is, currently Veronica isn't fine. She's in a coma due to poisoning, and the Duke's house can't afford to have her AWOL right now due to current events (like the King's feast) or else Veronica might lose the chance to become Empress. If word went out that she's in a coma due to poisoning, it will also ruin her image. Therefore, they need a body double to put the rumors of her absence to rest.