You could also apply Stroke>Dashes to the offset white stroke/nofill path (stroke equalling the dot diameter, using Dash = 0, Gap = (approximate) distance, and Round Cap.
If you have less than CS6, you may also apply the free Adjust Dashes script for an accurate even distribution (of the dashes/dots); it is available here:
-Do you have to create the scatter brush, or is that a default?
-Also, how do you enable it so that scatter brush can be selected for the stroke (like you have an additional dropdown to the right of the stroke dropdown where you can see it says the word "Scatter."
If you don't mind my asking, how do you do the same effect with a regular white line stroke (again with some space from the edge)? I tried playing with adding an inner stroke from the appearance palette and then another fill on top but that didn't work.
See the manual on how to crete brushes. You have to select the brush from the brush panel after you created it.
In order to make this with a normal stroke, make it round caps, dashed, with dashes set to 0 and the gap min double the stroke thickness.
The instructions you have for a normal stroke still keep it as dots. I just want a line. And how do you create space between the stroke and the edge? Where is the control for that?
Just create a stroke and give it color and thickness.
Add the effect "offset path" to the fill and make it bigger. Move fill below stroke if it not there already. See instructions on how to use the appearance panel in the manual.