How can I create a new window from within QML?

There is no way to create top-level windows using only built-in QML functionality.

However there's a project on Qt Labs called Desktop Components, which among other things contains a Window component, which allows you to create new top-level windows.

You can do it by using Qt.createComponent. Example (using Qt 5.3):

main.qml

import QtQuick 2.3
import QtQuick.Controls 1.2

ApplicationWindow {
    id: root
    width: 200; height: 200
    visible: true

    Button {
        anchors.centerIn: parent
        text: qsTr("Click me")

        onClicked: {
            var component = Qt.createComponent("Child.qml")
            var window    = component.createObject(root)
            window.show()
        }
    }
}

Child.qml

import QtQuick 2.3
import QtQuick.Controls 1.2

ApplicationWindow {
    id: root
    width: 100; height: 100

    Text {
        anchors.centerIn: parent
        text: qsTr("Hello World.")
    }
}