In addition to the answer by @Muckle_ewe, there is a the static function QFileDialog::getSaveFileName, which will present the standard open / save file dialog and allow the user to both select the path and input a name for the file.
It's definition is this: -
QString QFileDialog::getSaveFileName(QWidget * parent = 0, const QString & caption = QString(), const QString & dir = QString(), const QString & filter = QString(), QString * selectedFilter = 0, Options options = 0)
An example of its usage is: -
QString fileName = QFileDialog::getSaveFileName(this, tr("Save File"),
"/home/untitled.png",
tr("Images (*.png *.xpm *.jpg)"));
As the docs state,
This is a convenience static function that will return a file name
selected by the user. The file does not have to exist.