Having just gone through a Trans Tasman Agreement conversion, the NZ CAA are a breath of fresh air compared to CASA. To place a recent conversion on my Aussie licence took two months. Took our Kiwi cousins 7 days.
CASA sent me a blunt and to be honest, quite rude letter, because the application had no attached 'sticky label'. "This application is considered closed" they snarled. The Kiwi application was just a photo copy and again with no label. (a mistake by Qantas, not me) As I said, all fixed in 7 days. Subsequent dealings with the NZ staff on the phone was very pleasant. CASA wouldn't even answer.
Your CAA is fine by me. The plastic card licence is a little 'Mickey Mouse' though.