Measuring elapsed time in QML

As explained in the comments, QML Timer is not suitable for your specific needs since it is synchronized with the animation timer (further details here) and thus its resolution is dependent on animation timer as well.

@qCring solution is for sure satisfying and I would prefer such an approach, if an higher precision is needed or a better performance (see also this answer and the interesting link at the bottom about improving precision).

However, given your requirements, a pure QML/JS approach is perfectly feasible. In this case you can exploit JavaScript Date, both because it's easy to calculate elapsed time, using getTime(), but also because QML fully supports JS Date and also extends it with some useful functions.

Here is a simple example:

import QtQuick 2.4
import QtQuick.Window 2.2
import QtQuick.Layouts 1.1
import QtQuick.Controls 1.3

ApplicationWindow {
    width: 300
    height: 300
    visible: true

    property double startTime: 0

    ColumnLayout {
        anchors.fill: parent

        Text {
            id: time
            font.pixelSize: 30
            text: "--"
            Layout.alignment: Qt.AlignCenter
        }

        Button {
            text: "Click me!"
            Layout.alignment: Qt.AlignCenter

            onClicked: {
                if(startTime == 0){
                    time.text = "click again..."
                    startTime = new Date().getTime()
                } else {
                    time.text = new Date().getTime() - startTime + " ms"
                    startTime = 0
                }
            }
        }
    }
} 

Unfortunately, the QML Timer doesn't provide a property to check the elapsed time. But you could write your custom Timer in C++ and expose it to QML:

MyTimer.h

#include <QObject>
#include <QElapsedTimer>

class MyTimer : public QObject
{
    Q_OBJECT
    Q_PROPERTY(int elapsed MEMBER m_elapsed NOTIFY elapsedChanged)
    Q_PROPERTY(bool running MEMBER m_running NOTIFY runningChanged)
private:
    QElapsedTimer m_timer;
    int m_elapsed;
    bool m_running;
public slots:
    void start() {
        this->m_elapsed = 0;
        this->m_running = true;

        m_timer.start();
        emit runningChanged();
    }

    void stop() {
        this->m_elapsed = m_timer.elapsed();
        this->m_running = false;

        emit elapsedChanged();
        emit runningChanged();
    }

signals:
    void runningChanged();
    void elapsedChanged();
};

After registering via qmlRegisterType<MyTimer>("MyStuff", 1, 0, "MyTimer") it's available in QML:

Window.qml

import QtQuick 2.4
import QtQuick.Controls 1.3
import MyStuff 1.0

ApplicationWindow {
    width: 800
    height: 600
    visible: true

    Button {
        id: button
        anchors.centerIn: parent
        text: timer.running ? "stop" : "start"
        checkable: true

        onClicked: {
            if (timer.running) {
                timer.stop()
                label.text = timer.elapsed + "ms"
            } else { 
                timer.start()
            }
        }

        MyTimer {
            id: timer
        }
    }

    Text {
        id: label
        anchors.left: button.right
        anchors.verticalCenter: button.verticalCenter
        text: "0ms"
        visible: !timer.running
    }
}

Hope this helps!

You don't mention in your question if the measured time is only for debugging purposes or if it will be needed for other calculations. Because if not QML offers a very simple way to debug the time spent doing various operations using console.time("id string") and console.timeEnd("id string").

An example using a Button would look like this:

Button {
    text: "click here"
    property bool measuring: false
    onClicked: {
        if(!measuring){
            console.time("button")
            measuring=true
        } else {
            console.timeEnd("button")
            measuring=false
        }
    }
}

This will print the time in ms to the console, and can be very useful to measure the time needed to execute some long operations in QML.