I just installed InDesign CS6 and was told there's a conversion from Quark to InDesign, but I haven't been able to find a menu to do that.
Try posting in the InDesign forum where the InDesign experts hang out
Moving this discussion to the InDesign forum.
InDesign natively opens Quark 3 and 4 files. To open Quark 5 and later you'll need Q2ID from Markzware.
And as with any sort of format conversion you should not expect absolute perfection in translation.