Agreeing, your "ornate" brass 1-piece "domed" button is definitely not Military. But due to seeming to have a raised-lettering backmark surrounding it's loop, I'd push your "domed" ornate 1-piece button's time-period back a few decades, to about 1800 into the 1830s.
If you can clean its back a bit more, enough to read the backmark, please tell us what it says, because that info could narrow down the time-range.