Having seen similar war of 1812 time frame buttons like the design of yours, i'd say the button dates sometime from the 1790s-1820s - perhaps the War Of 1812 time frame... I notice the back of the button is got a dome shape to it or maybe that is just the picture itself.. Does the area you are hunting in have any War Of 1812 activity? Adding the location of the button can help sometimes too.. The button in photo is a 1812 Royal Regiment of Artillery button with crown on it.
Edit: I just saw Iron Patch post about the correct ID. Typing @ the same time..