Is the queens birthday on June 14th?

Yes it is

Queen Elizabeth was born on the 21st April 1926. However the official birthday is celebrated on the first or second Saturday in June , It is marked by the ceremony of The Trooping of the Colour and the Birthday Honours List. King Edward the Vll moved his date in the hope of better weather. It may be said that the Monarch's official birthday is on the day the Morarch declares it