You can achieve this just with QFile [qt-project.org] class: create a file3.ogg then read both file1 and file2 while writing their content into file3.
You can also use QProcess [qt-project.org] to execute that command but this is OS dependant.

Thank you, deimos!

Be very careful, joining two or more videos as raw files not always works, not all video/audio formats accept a new data stream after it ends, and this method will not work with different formats.
The best way of achieving this, is transcoding the files with, for instance, FFmpeg [ffmpeg.org], you can run FFmpeg through QProcess [qt-project.org].