The good news is that writing a http GET command is very easy in Qt.
The code in the documentation is pretty much all that you need: QNetworkAccessManager
So, something like this should do it:
Note: I wrote that off-hand so it probably won't compile.
QNetworkAccessManager *manager = new QNetworkAccessManager(this);
connect(manager, SIGNAL(finished(QNetworkReply*)), this, SLOT(replyFinished(QNetworkReply*)));
void myClass::replyFinished(QNetworkReply* aReply)
// Do something with reply