A rubber duck was a duck-shaped toy usually played with in the bathtub. They were sometimes made of plastic.
The Doctor had a rubber duck which he sometimes kept in the TARDIS swimming pool (PROSE: Evolution, Reckless Engineering) and sometimes in the bathroom. (PROSE: Lungbarrow, Seeing I) Shortly before arriving on Olleril, the Seventh Doctor played with his rubber duck in the jacuzzi. (PROSE: Prelude Tragedy Day)
The Sixth Doctor, while visiting Devon in 1929, had a rubber-duck shaped key in his possession. (PROSE: Timeshare)
The Doctor's house in Kent had a rubber duck in the bathroom. (PROSE: Cat's Cradle: Warhead)
Besma Grieve owned a rubber duck (PROSE: The Year of Intelligent Tigers), as did Vasar. (AUDIO: The Draconian Rage)
The Eleventh Doctor pulled out a rubber duck while searching for his missing sonic screwdriver. (COMIC: Sonic Sleuth)