Is there a Qt function to move files to Recycle Bin instead of truly deleting them, for OSes that support it, or do I need to use OS-specific code?
Since Qt 5.15.0 Alpha, this method has been added, which should be what you were looking for.
bool QFile::moveToTrash()
The corresponding code changes can be found here.
(This issue is old and the corresponding Bugreport at https://bugreports.qt.io/browse/QTBUG-47703 has already been posted, but I currently lack the reputation to comment, and found this to be a useful information.)