It's impossible to say if the software handles QIC format, since the official website is out of business. I've also tried to download the software from other websites, but they all had links back to the official website making it impossible again.
If you have the application, then simply install it and use the main menu to open the files, then you can see the supported file formats.
I recommend using other solution to back up your PC. It's called EaseUS Todo Backup and you can download it through the following website: http://easeus-todo-backup.software.informer.com/download/