I should just give you my email address, shouldn't I?
Yes, you do, but only after the birth usually. It's CYH (Child & Youth Health) who do it, I think they're just called nurses. Or midwives. Not Health Visitors though.
They gave me the form to fill out as part of the hospital admission forms (I think at the antenatal visit the week before I delivered - that antenatal was done at the hospital itself). It's not compulsory, and I turned it down, but they won't tell you that (and it sounds like you want the visit, so forget I said it, but it's worth knowing) with your details so they can come visit.
The first visit is within the first two weeks, I'm not sure when because I didn't have one. My friend did though, and it was a very long visit (I was visiting) about feeding and weighing and coping, and also the nurse gave her a lot of information about the local antenatal group. So at that visit, I think you'll be told about registering for any antenatal groups, etc., that you need. The antenatal groups run by CYH are quite structured; include 'lessons' on feeding/changing/settling etc., they're not just coffee mornings.
If you want less structured antenatal groups, look at the Australian Breastfeeding Association, they have meetings all over the place and specifically say that FF's are welcome too if that's what you end up doing. Never been to one myself but have friends that like that sort of thing.
CYH run clinics all over the place and you can go there and talk to someone either by appointment or they have drop-in hours. This is their webpage The one near us says it's for children up to 5, I think.
Oh, part of the reason I didn't agree to a visit was because my hospital also sent out their own affiliated midwives/lactation consultants in the first week, and I was more comfortable with them for a number of reasons, including that they are way less bureaucratic. She came out on day 3, then came back a week later to check that I'd stopped crying (baby blues), and she was lovely and low key.
Lastly (phew) registering the birth is done with help from the hospital and in the hospital if you know the name right away. So don't worry about that bit.