It's been mentioned several times that the horse that Tommy has bought with the intention of it running in The Derby is female - but surely female horses run in The Oaks, not The Derby? The Derby is for three-year-old males.
And just to answer some of the questions, the horse being female is mentioned in episode 4 when May comes to meet Tommy. Tommy says, "You came here to get my girl, right?". May says, "She looks in very good condition."
Six fillies have won the Derby. The most recent was Fifinella in 1916, who also won the Oaks. The other 5 were Eleanor (1801), Blink Bonny (1857), Shotover (1882), Signorinetta (1908), Tagalie (1912).