When we think of circuses, we usually think of exotic animals: lions and tigers and elephants.
But the first animals that were used in the early circus in the United States were not those exotics (especially then). The first elephant l did not come to this country until 1794. One elephant was brought from the Orient (which covered India, China, Japan and more then) by the Salem merchants.
No, most of the animals that would have been used in a circus were more homey. Dogs, pigs ( like the pig used by Billy the clown in A Circle of Dead Girls), and maybe bears. Horses were the stars for many years since the circus begun by Astley in England had begun as an equestrian show.
Some of the primary sources I read quoted farm boys who went home after the circus and tried to train their farm horses to circus tricks.