Hi there,
Nice to see another clin psy on the forum - and moving to Melbourne too! I'm going on a different visa (state sponsored 176) but hopefully can help a little with the paperwork and registration hoops to jump through.
Firstly, yes, get your qualifications recognised by APS - their website is quite clear about what documents they require and they're not as strict about who can certify them as AHPRA (i got a solicitor to do it - this is not acceptable for AHPRA...see next step!). I had to do this for my visa so it was first thing i did - I suspect you need to have it first too, before you apply to AHPRA (the next step).
AHPRA is for both registration as a 'psychologist' and then endorsement as a 'Clinical' Psy - i found getting the 'psychologist' bit a lot more straight forward than the 'clinical' - they want all sorts of letters from supervisors, logs of CPD and supervision, letters from HPC and BPS and copies of your transcripts sent direct from those organisations. They're a little pedantic and it takes time (about 3 months) but i got there in the end. I'd definitely advise starting these from UK as they can take time and i don't think employers will look at you until they are in place.
As regards job prospects - I don't arrive til mid-August and I already have 2 job offers (after applications direct over internet and skype interviews). Both for permanent posts, one in public health and one in private, and one is a job i've been dreaming of (yeay!!)...so i'd say personally job prospects are v good. The pays not as good as NHS - that said, i'm waiting for formal written offers as there seems to be a few added extras (annual leave loading, super and salary sacrificing) that i don't really understand the implications of but think will bump the overall package to being more similar.
Hope that helps but do ask anything further - and good luck with the move.