This is where I point out that in 1933 every American made the Bellamy salute during the Pledge of Allegiance and it looked very similar to the Nazi salute. This was done up until 1942 when it was changed.
The Nazi salute did come to have negative connotations, but in 1933 the gesture was not yet universally reviled like it is today.
Certainly at least one of the Queen's relatives was a Nazi sympathizer but I doubt a 7yr old Elizabeth was a Fascist!