Yes , you can.
A boat can travel between Australia and New Zealand, but it will need to be fully deep ocean capable.
You can book passage on a tour boat to travel there, or you can charter a private expedition from New Zealand, Australia, Chile or Argentina.
Boat.
By boat or by plane
There was a exodus of Vietnamese people called the boat people to Australia and New Zealand.
A fairly fast boat could travel from New Zealand to Australia in just under two days. Most cruise ships take two days plus.
im still living in Australia
about 5 hours
There are no ferries between Australia and New Zealand. However there are various cruise lines that operate. Another way is to travel by freighter, or cargo ship. These ships often have comfortable cabins for paying guests.
There is a travel agreement between Australia and New Zealand. No visa is required if you have a New Zealand passport, no criminal records, are treated for tuberculosis, and have not been deported, excluded, or removed from any country before.
You can fly commercially to New Zealand, Australia, Chile, Argentina or South Africa, then charter a private excursion -- all of which you'd pay for -- to take you to your Antarctic destination. Otherwise from one of the countries listed above, you may be able to find a tour that will take you to the continent.
New Zealand & Australia