I'm also a Brissie girl (kinda), just moved back after 9 years in UK.
I'm in the process of finding playgroups - there are two regulars close by plus, apparently, a random one. We drive a lot but that is because we only go to my sister's and to a nearby shopping centre (too near to bus, iygwim). Dh buses into town for work though.
A thing I think worth mentioning is that Brisbanites are very open, approachable and friendly, at least compared to where I was in Wales. People will talk to you in the park, shops, anywhere, and you can just walk up to strangers and ask them stuff, usually they don't mind and the problem will be getting them to shut up after you've got the info (or realised they can't help).
And the other thing is, because of the weather there is a LOT to do outdoors (and free!) - places like Southbank, lots of outdoor play areas, parks, Mt Coot-tha, various Forest Parks, Nudgee beach, Redcliffe/Shorncliffe, North Pine dam if you're headed further north, etc. etc. And you will invariably find someone to chat to. We are finding that aspect of living here quite marvellous.