Is there anything in the british protocol that says that a new king first time out of the country must be on an official visit ?

F.i., if so Charles could not go skiing in Switzerland or Austria (does he still ski ?) on a private absence if before he wouldn pay any official visit abroad.

BTW is there any official visit scheduled ?

The world has changed a lot since E II accession to the throne.
Was there a country that used to be the first the new king traditionally paid a visit ?

Which was the 1st country Elizabeth II officially visited at the beginning of her reign ? Any country of the Commonwealth ? Australia, Canada ? Or any other outside the Commonwealth ? USA, France ?