Well, since the Duchess of Cambridge actually exists and Prince Harry's wife does not (yet), I would have to say no, at least for the time being.
The current Duke and Duchess of Rothesay are Prince Charles and his wife, Camilla.
Camilla, Duchess of Cornwall.
Catherine, Duchess of Cambridge
Prince Harry is not married
Crown Prince Charles, as Prince of Wales, is also duke of Rothesay. His wife Camilla is the duchess.
No. She is Duchess of Cornwall.
Prince Charles and his wife Camilla are known as the Duke and Duchess of Rothesay when in Scotland,
Prince Charles' son William is married to Catherine,Duchess of Cambridge, but his other son Harry is not yet married.
Kensington Palace is one of the homes of the British Royal Family. It is the official residence of Prince Harry, Prince and Princess Michael of Kent, the Duke and Duchess of Gloucester, the Duke and Duchess of Cambridge, and the Duke and Duchess of Kent.
Catherine (Kate) Middleton, she is also Duchess of Cambridge as Prince William is now know as Duke of Cambridge.
His Royal Highness Prince William of Wales, Duke of Cambridge and Her Royal Highness Catherine, Duchess of Cambridge