If a planetoid was wet and you spun it would the water move to the equator? If the moon was alone in space and covered in X feet of water and it began to rotate would it displace to a bias along the equator? 
 A: It depends, and the specific parameters are made ambiguous by the example you're using.

If the moon was alone in space and covered in X feet of water

Specifiers that are really important:


*

*Density of the surface moon rock relative to water

*Does the planetoid have a molten interior?

*Are we talking about right away or over a billion years?


The hydrostatic assumption, which is used to describe planets in the Newtonian sense, predicts that materials will stratify according to density.  If this is taken as gospel, then we have contours of constant pressure that lie on a material boundary.  However, there are several ways that it won't go so simply in practice.
Imagine moon rock with a specific gravity of 1.0.  If you spun-up that planetoid, then the water would move, and the rock would remain stationary.  It has no physical force causing it to move.  But for that matter, the rock could float around anywhere in the ocean without any forces compelling it to go one direction or the other to begin with.
Then again, we might just declare the moon to be rigid.  Sure, there's a molten center, but this is a long distance from the surface layer mechanics which are relevant here.  So the water can move without the rock moving along with it.  This leaves some stresses in the rock.  If you are a mermaid on the moon's (former) surface, then you will feel a non-normal gravity.  In other words, the surface will feel inclined.  On the other hand, a sailor on the surface of the ocean will feel perfectly normal gravity under all conditions.
If the ocean is sufficiently shallow, it could feasibly pool along the equator and dry up closer to the poles.  In the rigidity assumption, this is because the rock doesn't move.  In the assumption that the rock density equals the water density, the water moves to the equator simply because it's more mobile.  But the rock material might still deform around the poles, in order to still form the perfect hydrostatic ellipsoid shape.
However, if we assume a sufficiently molten interior, and rock material heavier than water (which is reasonable), then over a long period of time, the water and rock will reform to create a water-world again.
