I haven't verified this personally yet as I'm still early on getting a diagnosis for this, but I was told by a lady from Adelaide who has Autoimmune Autonomic Ganglionopathy that rituximab is available in Australia to treat this, fully covered by Medicare in a public hospital.
As it's not a mainstream treatment for AAG either, I'm presuming that it might be able to be accessed for other types of autonomic or autoimmune dysautonomia so if you have something along those lines as well as a co-morbidity of CFS, you might be able to sneak in the back door by not seeking it purely for CFS.
Not too sure of the procedure at this point but I gather you also need to have the approval of the Therapeutic Goods Administration through the 'Special Access Scheme' which basically just involves the exchanging of letters from a medical practitioner which can be handled by your hospitals' treating doctor.