Hi Bob,
I did Singapore, Australia & New Zealand in one go last year with JY. I note that you said that you could not afford to do in one go. Because of the considerable distance I opted to do just that. There is a lot of travelling to that part of the world and once you are in Australia and New Zealand you seem to be travelling all the time also.
For me the trip was a "once in a lifetime" experence. I do not think I will be doing anything like that again. If I was you I would consider doing it all in one go!
I enjoyed New Zealand more than Australia infact, although would not have missed seeing the sights of Australia. Glad I have done it. My last experence of Australia was in 1971 when I visited Perth (Freemantle) with the Navy. Seeing the rest of Australia was an achievement I wanted to complete along with New Zealand.
All the best to what you decide,
Eric