It is a "Patriotic Motif" civilian horseharness rosette, from the first half of the 1800s.
Sidenote #2:
This rosette has only eight stars. An actual Military-issue rosette would have the correct number of stars for that time period. Note also that there are several varieties of civilian ornamentation on the rosette's outer rim.
Sidenote 1:
Some people have said it is a Confederate rosette, because the eagle's wings are drooped instead of raised overhead. Sorry, but early-1800s US patriotic emblems often showed a droop-wing eagle. For example, see the two different versions of droop-winged eagle on the early-1830s "Jacksonian" buttons in the photos below. One is at the upper right in the group-photo. The other photo shows the front and back of a different Jacksonian Patriotic droop-winged eagle Jacksonian button, and this one's backmark spelling the word color as colour means it was made in Britain.