Went to GP on Wednesday. When I showed him the name change paperwork and pointed to the reason comment he was quite “… really? … wow… Ok then.” Then spent about 40 mins trying to find someone to refer me to. 
; But he wouldn’t give me a letter needed for www.passports.gov.au/web/sexge… without seeing someone else as well. He doesn’t have any recent experience on the subject. :/
I finally heard back from genderrights.org.au/ with some local MD recommendations yesterday. After checking the locations, the clinic the GP referred to is closer and somewhat easier to get to.
I should call to make an appointment next week. Hopefully they have an opening for Wednesday after work. It appears to only be open 3 days/week, and 2 of those days aren’t good with work. Much easier to get away from work early with everything done on Wednesday then on Tuesday or Thursday.
Had planned to go to the BDM shopfront today to put in the name change paperwork, but it took a while for them to confirm I had enough documents for it that it was too late to get the bus out there before they’d close. Will have to see about leaving work early on Monday.
I’ve been talking to the area HR specialist over email, kinda anonymously, but if she thinks about what I’ve told her, she should be able to work out who I am (or at least cut it down to a handful of people). I was asking about putting a name change through the work systems, but keeping it confidential from people in the store until I was ready. Doesn’t appear like that will be possible though. 
I really hope I can get what’s needed to get the passport sorted out. I have travel quotes on hold for my holiday pending passport renewal, and it seems quite silly to renew the passport with current details for a single trip, then change it next year. Looks like either way, I’m going to have to pay extra for the express passport processing, since it will have to be done in a hurry in early September.