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If you set the AF square (for single-point AF) to be roughly the size of the moon, and then put that square ON the moon, it should nail focus just fine. The Low-light AF should not kick in. As Paul said, you may have to adjust your exposure to get the moon exposed correctly (I use aperture-priority).
But this also probably depends on your focal length. I assume you are using some kind of telephoto lens.
Also, my advice above assumes you are trying to photograph JUST the moon against a dark (or even not-so-dark) cloudless sky. On the other hand, if you are trying to capture the moon at night when it is partially obscured by clouds, that is a tricky shot, in that it is a very high dynamic range scene beyond which the sensor can capture. So either the moon is too bright or the clouds are too dark. In that case, you can do two exposures and try to blend them. But in the shot of the clouds, the overexposed moon will flare causing it to appear slightly larger than it actually is. So when you overlay the properly exposed moon over the cloud shot you end up with a halo around the moon. The only way I've been able to overcome that is to slightly scale up the moon in Photoshop. It's cheating, but not by a huge margin. And even then the result is just so-so, unless you are a master at blending, which I am not.
Which is why I gave up trying to capture such shots. But perhaps others can suggest better methods.
In cases of "over exposure", use manual exposure, and check the image afterwards, and make corrections accordingly for a new exposure accordingly.
You can use other profiles, to reach a more wide high dynamic range, to overcome high contrast.
Use "High Dynamic range" settings, and e.g make use of exposure bracketing.
Exposure bracketing and combining / blending several images, make use of a tripod.
I remember just using f8, ISO 100 1/125s or something on 450mm full moon only images which always worked.
Only so many of these you'll ever do as nothing changes except colours with bloods etc. Other phases of the moon cast longer shadows and can enhance zoomed photos. As long as you don't obliterate the highlights you are good.