I move emails to other labels in my gmail account on my TouchPad all the time. Can you see your other labels under Google in the Accounts tab? Possibly you may not have Show in IMAP checked for your labels in GMail settings.
Quidquid Latine dictum sit, altum sonatur.
Palm III -> Palm V -> Viewsonic Pocket PC V36 -> Treo 650 -> Samsung i760 ->
Palm Pre Plus -> Palm Pre 2 > Samsung Galaxy Nexus & HP TouchPad
Android 4.1 - Samsung Galaxy Nexus
CM9 Alpha 2 Official Nightly w/WebCM9 0.4 - HP TouchPad