Download a trial MQ server from IBM (to some hosts or VMs? that won't matter if you break them...), and (optionally) add a WMB in front of it to transform some messages and fire some messages at it from a GUI client via another broker?
so you 'could':
ia92 java gui to fire messages->microbroker(or rsmb or mosquitto)->WMB(optional)->MQ
have a look at the messages arriving on MQ via Websphere explorer (or its command line client, try googling for 'websphere MQ quick reference card') have a fiddle about with its subscriptions etc
and then start consuming those messages from its queues on the 'other' side of the chain via a WAS and then a java client
MQ->MQ(bridge maybe)->WAS->some JEE client you've written
don't forget the red books, keep it simple and then keep on adding complexity e.g. encryption etc.