Carrots were a common vegetable found on Earth.
Peri Brown once found herself in a dimension modelled on a combination of the Alice in Wonderland book she had been reading and the salad she had been eating. Among the creatures she met in this world was a talking carrot, who was horrified to learn that Peri had eaten carrots. (COMIC: Salad Daze)
Soon after his regeneration, the Eleventh Doctor found himself craving food and had young Amelia Pond produce different types of foods, most of which he rejected after tasting. He so despised carrots that he rejected them out of hand, without even tasting them. (TV: The Eleventh Hour)
Andy Stone in 2059 was the first of the Bowie Base One colonists to be infected by a mysterious life form, most likely through consuming a carrot washed with the base's contaminated Martian water supply. (TV: The Waters of Mars)
The Eleventh Doctor accidentally used a carrot to threaten a group of Wanters when he had meant to use his sonic screwdriver. He instead tossed the carrot at them, distracting a portion of them. (PROSE: Shroud of Sorrow)