Noting the tiny horizontal lines running across the entire front of the button (including the ribbon in the eagle's mouth), it appears to be an imitation of the 20th-century US Army "Great Seal" button, manufactured for use on civilian clothing. Also, your daughter's button appears to have a "self-shank" tinplated iron back. I've never seen that kind of iron back on an actual US army Great Seal button. (But I don't believe I've already seen every variation of those buttons.)