Not dorky at all.

I've been using the Gender Centre for the last year or so, primarily to take advantage of the free counselling sessions. They can be a good source of info for services in Sydney. I haven't used their social get togethers or support groups. But still, you might find these useful for getting started, so to speak.
This is my second run at transitioning, the first time was twenty years ago and just didn't work out for a range of reasons, mainly lack of confidence, youthful angst and no support networks. This time, older and wiser, with reasonable confidence, I decided I'd also make sure I had the support networks. Susan's has been very useful but so has the Gender Centre. Some people don't find that, so your mileage may vary.
My first time out the door as Grace was also to take the garbage bin out (at night!) but that was just to help me get over the going through the door concerns. The next day I went out, through a shopping centre, caught a train from a busy station and went in to the Gender Centre for a counselling session. It was very liberating, not least of all because I realised the previous transition attempt had not been for naught, I still remembered how to pass. Of course, you don't have that previous experience, but if you've managed to get through the door the rest of it will come in time too.
Are you on HRT, or is that still to come? Have you started looking into hair removal, especially your beard? Posture, walking and body language are also useful things to know the general difference between men and women. YouTube can help with those issues, and voice training and make up tips.