I suspect the reason VA flights to NZ aren't bookable on DL.com is because DL.com only supports destinations where Delta flies to or has codeshare flights to -- and apparently DL does not offer codeshare service to NZ. I agree it's annoying, as are many things about the Delta site, but at least you can search for long-haul and domestic VA awards on the site, which gives you a starting point for a conversation with an agent. (When you do end up calling an agent to book, I would recommend calling during normal business hours, which is when the most senior agents are scheduled to work, and not at a time when there might be any weather events affecting Delta's network, which would make the agents stressed and in high demand. You may have to call back a few times to get an agent who is able to work with you to do the booking, as they don't all know the ins and outs of partner award bookings very well.)
For booking short-haul flights separately, the best options are likely BA's award chart to book awards on QF, or ANA's award chart to book awards on NZ. You can sign up for a free BA Executive Club account and search for awards without needing to have any miles in your account, so you can see how many miles it would take and what surcharges they apply, and then decide whether you want to go ahead and transfer MR points. For ANA, you could do a similar process, though you have to trick the ANA website into letting you see partner availability -- see:
http://thepointsguy.com/2011/06/how-...-availability/
Keep in mind, first prize is if Delta will let you add on VA flights AUS->NZ to your long-haul booking for no additional miles, which should be doable. You'd only want to bother with separate QF/NZ bookings via BA/ANA if you can't get that to work, or if you end up wanting to add additional flights/trips above and beyond what Delta will let you book.
Finally, I came across this thread while searching for something else, and it has thoughts on a number of your questions, so probably worth reading in some detail:
http://www.flyertalk.com/forum/delta...after-syd.html