Elsewhere, the Princess Royal reminisces about taking her first trip aboard the Royal Yacht Britannia with her brother Prince Charles as children, following their parents' post-Coronation Commonwealth tour. The network released a teaser trailer for it, though, that sees Markle smiling as she examines the detail on her delicate veil, which was embroidered with the national flowers of each Commonwealth country.
A few months ago a fan video surfaced of Meghan introducing herself to onlookers, and the internet went into a spin over her apparent British accent.
According to writer and royal family friend Lady Colin Campbell, Markle's "politics are an issue" for the Prince's inner circle.
Meghan can be heard saying: "53 countries, oh my goodness". "It'll keep us busy".
The two-part Queen of the World examines Elizabeth II's passion for the Commonwealth and how she is passing on the baton to the younger generation.
We also see cheeky imp Harry revealing that when he sees the Queen, he quite simply panics.
"You guys have spent way more time in Buckingham Palace than I ever have - and you've only been here two weeks", he reportedly says in the clip.
"Have you bumped into the Queen yet?"
You know what they say: You can take the grandmother out of the queen, but you can't take the queen out of the grandmother.
But she pointed out that Sally had predicted the couple would make a "special effort" for Harry to meet Meghan's father, Thomas Markle, something which does not appear to have transpired.
ITV's Jo Clinton-Davis said: "This film is a rare opportunity to see Her Majesty up close and behind the scenes in this role, which means so much to her and has been so significant for Britain and the Commonwealth".