Firstly, you don't need a 'fast' lens when shooting on a tripod. The reason is that when on a tripod, you can easily shoot at just about any shutter speed and get sharp shots (of things that aren't moving). But keep in mind that when on a tripod, you should turn your VR off.
Next, you have to realize that the moon is quite bright. The part of it that we can see, is lit by full sunlight. So essentially, it's as bright (or brighter) than something grey on earth, that is lit by direct sunlight. The rest of the sky is likely much darker...so much darker than there is no way that you could properly capture both in a single photograph.
So with that in mind, you have to think about exposure settings and what the camera is metering off of and whether you are using the auto modes or not. In other words, if the camera is seeing a little bright spot in a sea of darkness, it's likely to expose for the dark sky or at least somewhere in between. That will leave the bright moon as a blown out spot, which probably isn't what you want.
So unless you can zoom right in a fill the frame with the moon, you will probably want to avoid the auto modes and put the camera into manual mode. Then dial in an exposure that you might use during the day (Google for common settings when photographing the moon). If you expose for the moon, you probably won't get good detail in any other parts of your image...but that's just a consequence of the physics of photography and there isn't much you can do about it. You just have to make your choice and live with it.
It's not uncommon to photograph the moon separately from the sky (or scene) and then put the two photos together later (in Photoshop etc.)