Can you confirm that the Laird Sentrius RG191 LoRaWAN Gateway (AU Version) supports MQTT publishing?
Welcome to the forum!!
In short any gateway only provides a connection for LoRaWAN nodes to the TTS network. MQTT has to be access through another means, usually a webhook.
Though outdated this guide walks through the general hardware/software stack - and shows the information flowing from node to your dashboard/MQTT broker (Adafruit.io)
The Things Network, IFTTT, and BEYOND! - Tutorial Australia
If you are looking for a more local connection you could create your own Peer-Peer Lora network (with an MQTT integration)