You need to set the currentIndex as well.

testme.qml

import QtQuick 2.2
import QtQuick.Controls 1.1
import QtQuick.Window 2.0

ApplicationWindow {
    title: qsTr("Hello World")
    width: 300
    height: 240

    ScrollView {
        anchors.fill: parent

        ListView {
            anchors.fill: parent

            id: messageList
            model: messageModel
            delegate: Text { text: mytextrole }
            highlight: Rectangle { color: "red" }
            highlightMoveDuration: 0

            onCountChanged: {
                var newIndex = count - 1 // last index
                positionViewAtEnd()
                currentIndex = newIndex
            }
        }
    }

    ListModel {
        id: messageModel
        ListElement { mytextrole: "Dog"; }
        ListElement { mytextrole: "Cat"; }
    }

    Timer {
        property int counter: 0
        running: true
        interval: 500
        repeat: true

        onTriggered: {
            messageModel.append({"mytextrole": "Line" + (counter++)})
        }
    }
}

There is still some jumping to the first element and jumping back down for a fraction of a second.