Thanks to all of you.
I have no time to dedicate close to a day to implement and test a method to copy files little by little (although there have to be loads of code parts already implemented I'm sure). By the moment, If the user is copying a large list of files and wants to interrupt the process, the process will finish when it finishes to copy the current file at that moment, and will erase the previous files. If the current file is huge, the user is going to wait until the end of the copy.
We know now the behaviour of the Qt copy process, so in the future if it is a problem for somebody, we will have to implement the buffer...
Again, thanks!