Let me explain to you what is wrong with the commented following exemple:
class.hpp
#ifndef CLASS_HPP
#define CLASS_HPP
#include <QObject>
#include <QDateTime>
class DateCpp : public QObject
{
    Q_OBJECT
    public:
        DateCpp();
    protected:
        // QML dates are QDateTime in C++, not QDate.
        Q_PROPERTY(QDateTime fooDate
                   READ getDate
                   WRITE setDate
                   NOTIFY fooDateChanged)
        QDateTime date;
        QDateTime getDate() const;
        void setDate(const QDateTime & d);
    signals:
        void dateChanged();
};
#endif
class.cpp
#include "class.hpp"
DateCpp::DateCpp() : QObject(), date() {}
QDateTime DateCpp::getDate() const
{
    return this->date;
}
void DateCpp::setDate(const QDateTime & newDate)
{
    this->date = newDate;
    /*
     * You have to tell QML that the property value has changed.
     * For this, use the NOTIFY signal of the property. If you do not emit it,
     * the property will not by updated on the QML side.
     */
    emit fooDateChanged();
}
main.cpp
#include <QApplication>
#include <QQmlApplicationEngine>
#include <QtQml>
#include "class.hpp"
int main(int argc, char ** argv)
{
    QApplication a(argc, argv);
    // Do not forget to declare your object to QML. ;-)
    qmlRegisterType<DateCpp>("Foobar", 3, 14, "DateQML");
    QQmlApplicationEngine engine;
    engine.load(QUrl(QStringLiteral("qrc:/main.qml")));
    return a.exec();
}
main.qml
import QtQuick 2.6
import Foobar 3.14
Rectangle {
    id: rect
    // A QML date (treated as a QDateTime by the engine).
    property date rectDate
    /*
     * Binded to myDate.fooDate, but variables are at different memory spaces.
     * Will be changed together nontheless.
     */
    property date rd2: myDate.fooDate
    /*
     * Just like rd2 but it is the same object in memory, a kind of pointer
     * on DateCpp::date.
     */
    property alias rd3: myDate.fooDate
    // No "=" but ":" for property declarations.
    property date aDateProp: Date.now()
    DateQML {
        id: myDate
        // It is a kind of slot connected to the fooDate Q_PROPERTY's NOTIFY signal.
        onFooDateChanged: {
            console.log("The foodate is: " + myDate.fooDate);
            // Will trigger a signal and "onRectDateChanged" will be executed.
            rect.rectDate = myDate.fooDate;
        }
    }
    MouseArea {
        anchors.fill: parent
        onClicked: {
            /*
             * It is JavaScript. "date d" is consequently wrong here.
             * d will be a QML date (treated as a QDateTime by the engine).
             */
            var d = Date.now();
            d.setYear(2002);
            // Calls the fooDate Q_PROPERTY's WRITE method, i.e. DateCpp::setDate();.
            myDate.fooDate = d;
            /*
             * If DateCpp::setDate(); is not called here, you can still copy 
             * the property to modify what you want:
             *
             * var d2 = myDate.fooDate;
             * d2.setYear(2025);
             * myDate.fooDate = d2;
             */
            myDate.fooDate.setYear(2025);
        }
    }
    onRectDateChanged: {
        console.log("The QML property has changed: " + rect.rectDate);
    }
}
TL;DR:
- You are dealing with 
QDateTimes. 
- Use the NOTIFY signal to tell the system that the value has changed.
 
- No 
date d to declare dates in JavaScript. 
- There are not any "
=" in QML properties declaration but ":".