The footage also shows Prince Andrew on his way to visit his wife and new daughter.
A reporter is heard asking him: "You looked very worried earlier in the day, Sir?"
He replies: "Ah, that's because I was on my way to the dentist!"
Prince Harry and Meghan Markle are the proud parents to their son Archie Harrison Mountbatten Windsor.
The family introduced Baby Sussex by posing as a family inside Windsor Castle.
But it seems we've seen this moment before.
An old video has re-emerged of the moment Sarah Ferguson made a mistake when stepping out with baby Beatrice for the first time back in 1988.
In the YouTube documentary Sarah Ferguson, the Duchess of York, the narrator describes how Sarah, who gave birth to daughter Beatrice at the Portland Private Hospital, "made a mistake quite in character."
"On her way to the car she spotted someone in the crowd with a bouquet of flowers."
And in true Fergie style, she passed Beatrice over to her father, Prince Andrew, and rushed over to the crowd, almost taking a tumble on her way.
"She rushed over in new shoes," the narrator says.
The footage also shows Prince Andrew on his way to visit his wife and new daughter.
A reporter is heard asking him: "You looked very worried earlier in the day, Sir?"
He replies: "Ah, that's because I was on my way to the dentist!"