A pony was a type of small horse.
As a youth, Melanie Bush turned down the offer of a pony by her parents, instead asking for a pocket calculator. (PROSE: Business Unusual)
Lilly and Holly Frobisher told their father that they wanted a pony. (TV: Children of Earth: Day Two)
Maisie Pitt suspected that her grandmother had poisoned her pony. The Twelfth Doctor later confirmed this. (TV: Mummy on the Orient Express)