The Queen also reveals how she eats honey from the hives of her own bees, decorates her own Christmas tree and is quite hard to give presents to, with trees and roses named in her honour. Then, after a pause, she adds with a smile: "I won't be here though".
When the pair come across a sundial positioned in the shade which Sir David points out, the Queen seems surprised at the oversight.
"Isn't it good, yes", the queen says, before flashing a wide grin at a person standing off camera.
Whilst talking, helicopters began to circle overhead and interrupt the quiet conversation and that saw Britain's oldest reigning monarch joke, "Why do they [the helicopters] always go round and round when you want to talk?". "Had we thought of that, that it was planted in the shade?" she asks with a chuckle, adding: "It wasn't in the shade originally, I'm sure".
"The Queen certainly knows what's going on and certainly knows what's going on in the world of conservation".
"The Queen's Green Planet" will be broadcast in the United Kingdom on ITV at 9 p.m. on April 16. "Sounds like President Trump, or President Obama", she joked.
The Queen and Attenborough have known one another since the 1980s, when he worked as a producer on the monarch's Christmas speeches.
The two nonagenarians appear relaxed together, with little of the formality and rigid deference often seen in people addressing the monarch.
The Queen took the rare step of agreeing to personally escort Attenborough around the palace's tree collection for the documentary, which will air on Monday.
The snap, which shows the royal sisters in matching green dresses, was released as part of a new initiative to launch trees across the globe in the Queen's name.
"You know, I've been quite hard to give presents to, so", she says, drawing laughter from Attenborough.
"It might easily be, yes." she said.