Home Guard Dan is correct... it is a Jacksonian era (late 1820s to early 1830s) civilian-usage "Patriotic motif" button. Button collectors call this type of 1-piece brass flatbutton with an applied rim a Jacksonian button because they were popular during (and somewhat after) the presidency of Andrew Jackson. Jacksonian buttons were made for use on civilian clothing, not military uniforms, which is why your button is not shown in the Albert button-book. Here's a photo showing some of the many varieties of Jacksonian buttons. It was originally posted here in the What-Is-It forum by Don In SJ. Yours is shown at upper right in the photo.
After-posting edit: HomeGuardDan and I were typing at the same time. Took me a bit longer because I had to hunt for the photo. I didn't see Dan's second post until after I posted mine.