We can not support QTR of course. It's not our software. Roy Harrington is your source of support. The QTR users group may soon be abuzz over Mavericks.
But, to give you some perspective...at Cone Editions Press we have still, a blue and white Mac running OS9 which connects by SCSI to a Hell 3400 drum scanner. There is no support for this drum scanner beyond OS9 by Linotype Hell. We have an old OSX 10 version computer which runs a certain version of software that includes a Firewire to SCSI adapter so we can run it at 14bit. Those two systems are forever frozen or we have to ditch the drum scanner - and of course nothing compares to a Hell drum scan. So we keep them.
Our rule of thumb is to NEVER update an OS unless we verify first that everything we need runs on the new OS. Our preferred color management spectrophotometer has not been updated past 10.4.7 - on which it is last possible to run the DTP70 by X-Rite - so we maintain this OS as well. Always at the minimum, make a boot partition which you can revert back to. At this point you will need to be in contact with Roy Harrington of QTR. Hopefully he will have a speedy resolve for you. We will wait probably half the year until everything is worked out before updating anything to Mavericks. It is designed for the new Mac hardware. Every update is ALWAYS with its risks and Apple always tells you this in their fine print. They recommend you back up everything including the boot.
Even though we can not support QTR - logic says update your printer drivers and then try reinstalling QTR printer. We will be interested to know your experience and the resolve on this. Please keep us appraised of the situation!