Giuseppe is right, you don't need to use libcurl, curlpp and similar libraries.
There is no need for that, Qt has a simple and working class on it own.
Keep in mind that the standard way of sending request and retrieving reply is asynchronous.
You always have to connect the manager finished(QNetworkReply*) signal to a slot.
If you send multiple requests and don't want to add a slot for each reply, you can always run an event loop, and connect the managers signal to event loops quit() slot.
Something like this:
QNetworkAccessManager *manager = new QNetworkAccessManager(this);
QEventLoop *eventLoop = new QEventLoop();
QObject::connect(manager, SIGNAL(finished(QNetworkReply*)), eventLoop, SLOT(quit());
manager->get(QNetworkRequest(QUrl("http://stackoverflow.com")));
eventLoop->exec(QEventLoop::ExcludeUserInputEvents);
QByteArray replyData = reply->readAll();
... //do what you want with the data your receive from reply
Btw. don't know what are you doing. But if its a mobile app, I would recommend you switch from VS to QtCreator IDE. It has a nice simulator and a complete toolchain for mobile device testing.