Use the sunny f16 rule as a starting point and bracket. Remember that even though it is night out, the moon is in full sunlight and the exposure has to reflect it.

Ditto Larry. The camera is reading the dark sky and is therefore over exposing the subject moon. The shutter speed is too long and is recording the motion of th earth.
You are using a tripod, yes?

Thanks for your reply.

Yes, I'm using a tripod. And yes, the exposure was very long! I tried manual at Speed 500 and f/11. Should I keep it at P and just change it to start bracketing at f/16?

Set the camera on Manual and set the shutter speed as a reciprical of the ISO with the lens on f16. For example, if you use ISO 100, set the lens on f16 and the shutter speed on 1/100 second. That would be your starting point.

Program is reading the dark sky around the moon and taking it into consideration when it sets your exposure.

If you want color or detail in the sky, shoot when the moon is low on the horizon and try Program. If you want a perfectly exposed moon, use what I suggested and then crop out the moon and add it to other images.

I'll give that a try. Thanks for the info. It is greatly appreciated!