Konqueror 3.5.2 doesn't allow you any more to make a backup of an item in the same directory.
I already added an entry in the wishlist of Konqueror but, in the meantime, here is a service menu.
Right click on a file or a folder, give a new name and press RETURN. That's almost what we could do until version 3.5.1. (It also works for several items selected at the same time.)