All I am trying to do is create a simple 3d circle for icon use. However, the ball gets very grainy and unsmooth when I make it smaller. I need it to be 12 pixels by 12 pixels. Is there anyone that could assist me?

Making small circular objects should be not problem. If you are using 3D, make let the rendered source image be big enough and only resamle it to small size when turning it into icon in the last step.