The answer to your question is really simple, assuming that you're running live from the CD. Just make an icon for QTParted on your desktop, and for the command, put in sudo qtparted. Or edit its entry on the K Menu so that the command is sudo qtparted.

Probably work for all those other apps, too.

If you're running off a hard disk install, then there's probably no way around putting in a root password (you really don't want there to be, do you?).

Really though, the problem I was writing about was not that I was being prompted for a password, but that THERE WAS NO PASSWORD I COULD TYPE THAT WOULD WORK. Certrainly I can use the console and log in, but that rather defeats the purpose of having a program listed in the K menu: it can never run from there.
Of course not! If you installed any distro without setting a root password, you'd have the exact same problem. Since there are no default passwords set in Knoppix, you have to create a root password before you can use those programs from the K menu, by design.

Klaus could have altered the menu settings so that all of the programs that require root privileges ran from the K menu without asking for a password, but that would have required a lot of work to solve a problem that doesn't really exist.

(And I could swear that I didn't see QTParted on the menu anywhere when I ran KNOPPIX_V3.3-2004-02-16-EN. Sigh. It was kind of late.)