I'm an Aust RN and just passed NCLEX almost 2 months ago. Tho I did not get here through E3 visa, I may be able to give you some help with the NCLEX process.
I think you should be able to do this all yourself. You have plenty of time to get all the paper works and whatever is necessary to get started. If you already know the state you want to work in, then go through thier BON (Board of Nursing) and see the list of CES. Fill up the forms, pay their fees and send it off. From there, they will send off your report to the state's BON. Easy process but may take a while (mine did). The BON will then decide if you are eligible to sit NCLEX (again, mine took some time to process as there was some confusion with my CES report). You have 2-3 years to prepare for all these, so get started and maybe start planning for the test.
Again, get crackin' on the NCLEX part because is E3 visa is a whole 'nother story.
Hope that helps.