The dollar coin is not real gold. The coin is worth a dollar unless it is uncirculated you may get around $1.50. If the coin has the mintmark "S" then it is a proof and is worth around $6. The mintmark is located on the rim of the coin.
Do you want to check those dates again? 1881 has nothing to do with President Adams. If you have a gold-colored coin that's 26 mm in diameter, the dates will be 1797-1801 and it's an ordinary circulation coin worth ... ba DING ... one dollar.
The first thing is, it's not gold and it's not old. The coin is a 2007 (date on edge) John Adams Presidential dollar. The coins are made from brass, the dual date you see, is his term in office. The coin is just a dollar, spend it.