MQTT is a publish-and-subscribe messaging transport. There was a similar framework in the Qt Mobility stack called Publish and Subscribe, which is now part of the officially unsupported QSystems API framework, which also includes QSystemInfo and QSystemFramework.
QMqtt is a framework for writing MQTT clients. You will need to install and run an MQTT broker, such as Mosquitto or HiveMQ, or use an internet-based service. For my development and testing purposes, I chose HiveMQ. You can download it from https://www.hivemq.com/.
They also have a public broker at http://www.mqtt-dashboard.com/index.html.
MQTT has a broker, or server that one or more clients connect to. The clients can then publish and/or subscribe to different topics.
You can use QWebSockets to access a broker, and there is an example in Qt, which uses the WebSocketIODevice...