1833, "one who embodies the person or character of another;" 1840 as "one who infuses (something) with a personality;" 1842 as "dramatic actor, one who plays a part on stage," from impersonate with Latinate agent noun suffix. Meaning "one who imitates the manners and speech of another" for entertainment (by 1921) perhaps grew from older theatrical use of female impersonator (1876), male impersonator (1874), both once popular stage acts; the first example of the latter was perhaps Miss Ella Wesner, who had a vogue c. 1870: In Britain, blackface performers were called negro impersonators (1906). As a fem. formation, impersonatrix, as if from Latin, is from 1847; impersonatress, as if from French, is from 1881.
Her [Wesner's] impersonation were a genuine surprise and her success was so pronounced that in a short period a host of imitators made their appearance. Her most successful rivals were Bessie Bonehill, Millie Hilton and Vesta Tilley, all of London. [M.B Leavitt, "Fifty Years in Theatrical Management," New York, 1912]
There is no member of a minstrel company who gets a better salary than a good female impersonator, the line being considered a very delicate one, requiring a high style of art in its way to judge where fun stops and bad taste begins, with decision enough on the part of the performer to stop at the stopping place. ["The Ancestry of Brudder Bones," Harper's New Monthly Magazine, April 1879]
The most fascinating performer I knew in those days was a dame named Metcalfe who was a female female impersonator. To maintain the illusion and keep her job, she had to be a male impersonator when she wasn't on. Onstage she wore a wig, which she would remove at the finish, revealing her mannish haircut. "Fooled you!" she would boom at the audience in her husky baritone. Then she would stride off to her dressing room and change back into men's clothes. She fooled every audience she played to, and most of the managers she worked for, but her secret was hard to keep from the rest of the company. [Harpo Marx, "Harpo Speaks"]