According to Dickie Arbiter, former press secretary to the Queen, and noted Royal Expert, the heiress apparent will not have the style Duchess of Cornwall, as the eldest child of the Sovereign.
The title will remain for the eldest son of the Sovereign. The heiress apparent will have access to the duchy's funds through a Sovereign's Grant.
[It has not yet been stated if the heiress apparent will have the title of Princess of Wales and Countess of Chester or, in Scotland, Duchess of Rothesay.]
If baby Cambridge is a boy, the discussion of titles for an heiress apparent will be moot for at least another generation.