Shooting the big full moon is a common pastime for some photographers. Easy enough to do. Set you ISO to native (100 or 200 depending), F8 to F11 on aperture and start at 125th second. Helps to have have a relatively long focal length at least 200mm on an APS-C or 300mm on a full frame. Nothing to it. The issue I find (although I do have a lot of full moon pictures) is that the full moon tends to be a little flat. It’s kind of like taking a picture with the flash on the camera. No definition.
Last night just after sunset we has a Waxing Crescent moon that was only 7% illuminated.
I did have to adjust up the exposure as there just isn’t as much light reflecting off a moon at 7% compared to a full moon at 100% With the sun glancing off the edge of the moon you can get definition in the craters on the edge. And with less light overall you can also pick up a star or too. BTW what white balance do you use for your moon shots? Daylight of course. The light is coming from the biggest daylight source that we know.