Is it true that the movement of the turkey inspired a ballroom dance?

Yes, it's true. The turkey-trot, modeled on that birds characteristic short, Jerky steps, was one of a number of popular dance styles that emerged during the late 19th and early 20th century in the United States. The two-step, a simple dance that required little to no instruction, was quickly followed by such dances as the one-step, the turkey trot, the foxtrot, and the bunny hug, which could all be performed to the ragtime and Jazz music popular at the time. The popularity of such dances spread like wildfire, helped along by the teachings and performances of exhibition dancers like the famous husband-and-wife team Vernon and irene castle.