I believe it is not possible. The only way I have found to sort Quick Launch icons is to unlock the taskbar, then increase the size of it, and drag icons one by to the end of Quick Launch in the order you want to have them (at least my Quick Launch only let's me to move an icon to last position, not in between other icons).
An example. Here's my taskbar with Quick Launch:
To reorganize, I unlock the taskbar and make Quick Launch area bigger so I have some extra space at the end of it. I have vertical taskbar but the same works with horizontal.
Let's say I want to move the IE icon to be the last one. I drag it to the end, to that empty space and drop it there.
This, moving a QL icon to the end is the only way I've found. I seem to be unable to drop a QL icon between other icons, it always goes to the last position. I wanted mine to show browsers on top row, and Libraries, Computer and Trashcan as last icons, so I just dropped icons to the last position in that order I wanted, one by one from first to last.
I notice I'm telling this in a very confusing way
Hopefully you get my point here.