Kubuntu is the only Ubuntu flavor (I hate them for calling different versions flavors) that comes with QT installed by default.
Any Linux distro that uses KDE or Razor-QT will have QT installed by default, there is no reason for others to as they use a toolkit called GTK.
So, that means that to use the LiveCD approach you either have to use the non-GUI version or connect to the internet at least once to download stuff. Is there a big security issue with the latter option?
That LiveCD should work with QT out of the box.