I am using PLE version. I got eyes parented to head, but I need it to be on top in camera view so it will show. The nudge in z-space is alt+down arrow per the manual. Nothing happens. I also have the transform tool selected and I am in animate mode, all as instructed in the manual. I had the same issue with the TBStudio demo.
Am I overlooking something?
If its the same problem I had…its all a matter of clicking the whole thing before you move it. 
Its got to be selected.
I also had trouble using it, what I did was change the z-index on the later properties itself.
There are several shortcut styles, you would need to be set to the Toon Boom
Animate shortcut style not the Flash one which may use a different keystroke combination.
You can verify/modify your shortcut style from the drop-down menu of the
Shortcuts tab of the preferences at the very top of the page right under the tabs.