Welcome to FT WGTN1!
If you buy your RTW ticket in business class or first class you will get lounge access based on class of service, if you fly economy class you will not be entitled to lounge access.

Perhaps you can contact Air NZ member service and ask them if they would consider giving you the gold card before you leave if you can prove that your itinerary will indeed qualify you for gold and the ticket already has been paid.
I wouldn't count on it, but nothing to lose.

Otherwise you may want to consider applying for a Priority Pass which will give you lounge access at airports all over the world irrespective of airline and class of travel.