Im no expert but I think you just need to go into your local rta and tell them the situation... get the rego transferred into the NSW and into your name.. fees will apply.. not sure if you need to worry about the 4age swap.. tell them its been done and see what they say.. they may tell you to go get a pinkslip (I think) thats RWC isnt it..? because its now in NSW..
good luck anyway..