We've been through this process earlier in the year, and the steps are as nicolejoy outline above:
1. Get the birth certificate - the hospital should give you the info of where to go for this and a list of documents to take. Only one parent needs to go if you are married, and it will be processed in an hour or two.
2. Apply for Australian citizenship by descent (assuming that one or both parents are Australian citizens). This takes 10 working days to process. You will need a photo of the baby and for the form to be signed by someone who is a lawyer, teacher, etc (the usual list - check the form for details). For the citizenship application, they're not as picky re the photo as they are for the passport.
3. Apply for the Australian passport - I did this when I picked up the citizenship certificate, so needed to have all the forms ready as well as photos of the baby (they are very particular about these! Read the info they will give you) and the necessary witness signatures. Again, it takes 10 working days to process.
4. Obtain the HK visa in the passport from Immigration. A few more forms to complete as well as provide baby's birth certificate, your marriage certificate, parents' HKID cards, copies of visa stickers in your passport (I might be missing something here, but they will tell you at Immigration). Once you have all the necessary paperwork, this should be processed in a few hours.
For the passport photos, I went to one of the photo shops in Central and held my baby up so they could take the photo. They then used Photoshop or similar software to remove my hand from the photo. I know of others who've managed to take a photo of the baby when they are lying on a white sheet, but I tried numerous times and never got a decent photo myself.
Good luck with the delivery!!