The problem is that the model is not watching for fs changes, and not updating. And you want it to control at the higher level.
So, if you set your rootpath to my computer, it should work:
QString rPath = fileSystemModel->myComputer().toString();
fileSystemModel->setRootPath(rPath);
Here was a similar problem (changing filters didnt update model) solved this way.
Also, you should not have to resize the table with each change.
Just change the resize mode with:
void QHeaderView::setSectionResizeMode(int logicalIndex, ResizeMode mode)