I don't think there's any way to get a seperate virtual desktop on your second monitor (which what I think you want).
This was the first thing I thought of too when I got another monitor but when I thought about it a bit more I realised that it's rather poinless (for me at least). I don't know about KDE but if you're using gnome then the panel only streches through one monitor (so you can have another panel in the other if you want) so I figure since that's the only thing distinguishing having seperate monitors to having seperate desktops, it's virtually the same thing (pun intended
Think about it, two monitors is just as good as a seperate virtual desktop since windows will (in Gnome) behave in one monitor as if it was a seperate virtual desktop and not for example stretch accross both when you maximise them. Even better, you can "edge flip" between monitors as you would between virtual desktops except this way you can see where you're going.