One stopover should do you nicely, if you want to play safe and do any. This is on the basis that you can safely fly from UK/Europe to Australia/New Zealand (or the other way) without a stopover - thousands of people do it every day.

In fact, if you really wanted to do it in the minimum time and you can do it on lie flat beds, you really don't need a stop at all. Just plan some longer connects at airports like SIN where you have can access to a gym to get some exercise.