What would be the formal title for a daughter of a Duke and Dutchess?

Dutchette

The wife of a Duke is called a Duchess, the wife of an Earl is called a Countess. That is because Duke is based on a Latin word and had a feminine version. Earl is based on an Old English title and was purely military title. It has no feminine version. In later centuries an Earl was considered to be the equivalent of a Count in continental Europe and their wives began to use the title Countess.

The wife of a Prince is called a Princess, but she must borrow her husband's first name as well. For example the wife of Prince Michael is called Princess Michael (where her first name is not used). Since this convention is awkward for a modern woman, Prince William will probably be given another title upon marrying just so that his wife has a better title.

========================

The daughter of a Prince, Duke, or an Earl can use the title Lady.

Diana was born "The Honourable Diana Frances Spencer" because her grandfather was an earl. Just before her 14th birthday her grandfather died and she became the daughter of an earl. Her title was changed to "The Lady Diana Frances Spencer". She held that title until the age of 20 when she married and became "Her Royal Highness The Princess of Wales".

Upon her divorce she was no longer royal, but retained the title of "Diana, Princess of Wales". But she still had her title that she was given as a teenager. Sometimes if she wanted to be a little more informal she would go by "The Lady Diana".

===========

Normally you use the highest title to which you are entitled. Beatrice uses Princess Beatrice. She is also titled "The Lady Beatrice" as the daughter of a Duke and Duchess, but since she is also the granddaughter of the monarch via a male line, she is a Princess as well.

Some royals are using lower titles in recent years in an effort to avoid undue attention. Camilla, the Duchess of Cornwall simply does not want to use the title "Princess of Wales" since it would invite comparisons with Diana, so she uses her second highest title.

The youngest granddaughter of the queen (age 6) is titled "The Lady Louise" since her parents felt that it is easier for her not to be called The Princess Louise her whole childhood.

If William marries Katherine there is a slight possibility that she will opt for 'HRH, the Lady Katherine". She will simply wait until the Queen dies to use Princess of Wales. But she is likely to be in her 40's.

In the British peerage:

- the eldest son (the heir) uses his father's second-best title "by courtesy". (Every duke has lesser titles as well as his dukedom, because nobody ever got jumped from commoner to duke without being made up to a lower-rank peerage first.) So, the eldest son of the Duke of Bedford is the marquess of Tavistock, the eldest son of the Duke of Wellington is the Marquess Douro, and so on.

- The younger sons are all called Lord Firstname Surname; e.g. the fictional detective Lord Peter Wimsey, in the novels by D L Sayers, is the younger son of the Duke of Denver. (This formula is ONLY correct for younger sons of earls and above; no peer is ever called Lord Firstname Surname.)

- The daughters are all called Lady Firstname Surname. This holds for the daughters of marquesses and earls too: e.g. before her marriage to Prince Charles, Princess Diana (the daughter of Earl Spencer) was correctly known as Lady Diana Spencer, and was addressed in speech as "Lady Diana".

The oldest child tends to gain the lesser titles of a Duke. Most Dukes tend to hold other titles like earl so the oldest child would have this. other than that they can genrally be called Lord/Lady

If her father is a Royal Highness, she is known as Her Royal Highness Princess Mary. In conversation the title Your Royal Highness is used once, at the beginning: thereafter, Ma'am. (The name Mary is used as an example)

If she is the unmarried daughter of a duke who is not a Royal Highness. She is known as Lady Mary Smith. (the name Mary Smith is used as an example)

This is a question that is of concern only to people who do not as a rule mingle with nobility.

If you do have occasion to speak to nobility, treat them like rather splendid military officers and you won't put in a dungeon for life.

What's a "Dutchess"???? A female from Netherlands?

She's a duchess.