Usually, when a US Navy "style" button has an iron back, it is a civilian-usage imitation of the actual US Navy buttons. The imitations are known as "Fashion" buttons. The exception to the rule-of-thumb about ironbacked Navy buttons is the kepi-size (13-14mm) ironbacked US Navy button, made for use only on the Navy's version of kepi-hat. That seems to be what your button is.
More specifically, it appears to be the 1840s version of US Navy button -- because it is a 2-piece button (not a 1-piece), and it shows an upright spread-winged eagle standing atop a vertical anchor. Sidenote: the US Navy button's emblem was changed in the very-early 1850s, showing the eagle standing on a more-or-less horizontal anchor.