Hi
I'm a Child protection social worker and have found that social work jobs are thin out there.
I have sent out almost 20 applications over the last six months and understand that each post is receiving around 25 applications each.
I had some interviews but was advised that someone with local knowledge was the preferred applicant although they were very impressed with me etc etc.
Admittedly i am in a smaller city and you will probably have more luck going to Auckland.
Have you tried SEEK , to search for social work posts? Not sure about the learning disabilities field myself.
My understanding was that I could only register with the social work board once I was working and that it is not a requirement to begin working as a social worker here unlike the UK.
Also it costs alot of $$$ which some companies help with the process.
Good luck - you may want to start applying sooner rather than later.