The eight-month-old's outfit is from Rachel Riley, a British luxury children's brand based in Marylebone.
The company also has a store on New York's Madison Avenue.
The £75 "classic tailored dungarees" with a sailboat smocked design on the front panel have sold out in the six month and 12 month sizes on the company's website.
But mothers prepared to wait for their babies to grow into the outfit can still buy it in sizes 18 months and two years.
The company's designs "draw inspiration from the forties, fifties and sixties with fine tailoring, beautiful hand smocking, hand embroidery and vintage-inspired prints designed by and exclusive to the brand", according to a statement on the website.