The queen's grandson Prince William, Duke of Cambridge, is second in line to the throne after his father Prince Charles, Prince of Wales. His wife, Katherine, Duchess of Cambridge, is pregnant. Under the present rules, if her first child were to be a daughter and they subsequently had a boy, the boy would automatically become the next in the line of succession.
The British government has decided that the present succession rule is out of date and does not conform to the principle of gender equality. This view is shared by all Commonwealth countries, which have retained the queen as their head of state. Legislation will accordingly be brought forward to change the rule before the Duchess's baby is born.
So if she has a daughter, the daughter will be in line to succeed as monarch in the course of time. This change in the law is likely to be passed without dissent. Gender equality is now almost universally accepted. The established Church of England recently rejected the appointment of women bishops but this decision was due to opposition by a minority and is likely to be reversed.