Hi John.
If you look back to where your itunes library lives by default you will see a new itunes library. (documents on PC I think)
Playlists etc are stored here, and will not be stored on the NAS.
Itunes be default store music in itunes on the local drive you need to specify to itunes that its somewhere else by going to prefs and advanced. If you do not do this then new music added will get put in default location of the local drive.
For total sanity I recommend copying the itunes MUSIC folder to the nas, not the entire folder. Then in advance settings point to this music folder.
What you have done is made your playlists defunct by putting them on the nas, itunes will save playlists in the default location on your local drive.
This is the problem you are probably running into with the qute.
The qute is only getting the UPNP info from the nas, which no doubt is ignoring the playlists as this is a database used by itunes.
I assume a qute can't see an itunes playlist unless the the NAS can dish up said playlist via UPNP, you would need to look in the nas settings for that. However the playlist will not be 'live' as itunes will save your new plalist to default local location.
This has been got round before with hardlinks. in essence you have the entire itunes folder on the nas and on the local default location have a symbolic link to it, as if it were the actual folder (standard shortcuts won't work)
This all goes seriously tits up though if the nas for what ever reason is not available when itunes opens.