If you use the Galileo's IoT image, you will be able to follow Building and running Mosquitto MQTT on Intel Edison in order to set up Mosquitto for MQTT on Galileo. Even though the guide is originally written for the Edison it'll still work for you.
There's only one thing to point out from the guide, the line "add user mosquitto" should be "adduser mosquitto", so keep that in mind when testing it.
With MQTT is it possible to measure the payload size and the time it takes to publish and receive a message i.e. the latency?