History
In 1979, a young Western Australian boy named Harvey met the Tenth Doctor soon after stumbling across a kangaroo with glowing eyes. It turned out that the animal had been affected by the recently-fallen Skylab. (PROSE: Bennelong Point)
On at least one adventure with the Eleventh Doctor, Abigail Pettigrew went to Uluru and was photographed in front of a kangaroo crossing sign. (TV: A Christmas Carol)
Kangaroos were among the animals on board the Ark in circa 10,000,000. (PROSE: The Ark)
In the 42nd century, there was a TV show based off Iris Wildthyme's autobiography, Ugg Boots and Catsuits: My Fabulous Life, and Panda was replaced by an Australian kangaroo, Hoppy. (AUDIO: The Iris Wildthyme Appreciation Society)
Other references
Immediately after regeneration, the Seventh Doctor's brain was addled, and he unwittingly altered several common metaphors. He claimed that Melanie Bush had the "mind of a kangaroo" before she reminded him that people with great memories were said to have the "mind of an elephant." (TV: Time and the Rani)
The planet Aridus had blue kangaroo-like creatures. (PROSE: Warmonger)