While everyone has a different set of interests, perhaps you might want to do something more unique to Australia that sit on a beach over the weekend.

It is a very long flight. Both countries have a great deal to offer.

A search of the South Pacific topic may help you do a short cut on things to do and places to go. Same with trip reports on each of the cities you plan to visit/do business in. There are also great web sites.

I would also suggest you ask you doctor about the potential preparation for your child to insure you do not damage him/her by failing to insure everything is okay.