Unless a heiress apparent will be invested with the title Princess of Wales, I doubt she would become both Princess of Wales suo jure and Princess Royal.
There is absolutely no reason why William's eldest child, if a daughter, cannot be a Princess of Wales (assuming she ever becomes one) and The Princess Royal at the same time. It's not as though either title can be conferred upon younger siblings, so why not have both? Of course, she would be known under her highest available title - and The Prince(ss) of Wales pretty much outranks anything and everything else.
I would think that she would one day be Duchess of Cornwall and then Princess of Wales and Finally Queen. Traditional ways can be changed. For it to be a true change the daughter as well as son would get the same.
As things are right now, the female form of
The Prince of Wales is only used to designate the wife of the Prince of Wales. That may or may not change it future: time will tell. Of course, there are technically no legal obstacles for an Heiress Apparent to be created one - it's just never been done before.
The only time a woman came anywhere close to be The Princess of Wales in her own right was back in 16th century, whe
n Lady Mary (the only surviving child of Henry VIII and Catherine of Aragon) was briefly given all the rights and prerogatives of The Prince(ss) of Wales.
The Duke of Cornwall title (and several others) is different because the holder must not only be the Heir Apparent, but also the eldest surviving
son of the Monarch. For instance, if Prince Charles were to predecease Her Majesty, Prince William could be created The Prince of Wales but he'd never be the Duke of Cornwall.