Hi there,
Travel between New Zealand and any of the states in Australia in the years immediately before WWI can be difficult to track, simply because it was movement between British colonies in the era before ordinary folk needed to carry any form of identification. Passports were not issued to ordinary folk in Britain until 1914. So, in the same way that a person could move between any of the states of Australia without needing to carry identity documents, so too could that person move between any of those states and New Zealand. We should also remember that the Australian constitution actually allowed for New Zealand to be one of the founding states, while Western Australia was the colony that was initially the most hesitant to be in the federation.
Both Papers Past and Trove are extremely useful in following passenger movements across the Tasman, but you need to remember that the info in the newspapers is based on verbal advice given to the shipping lines at time of boarding/purchasing passage. Mr and Mrs Abc + x children MAY be the extent of the shipping line's info at the time. And as others have mentioned, not all shipping lines provided copy of all their manifests to the newspapers (and not all newspapers found room to publish those lists).
http://www.justice.tas.gov.au/bdm/family_history "Please Note: The Tasmanian Registry does not have an online search facility to access birth, death and marriage records. "
Here's the link to Papers Past (NZ digitised papers)
http://paperspast.natlib.govt.nz/cgi-bin/paperspastand
Here's the link to Trove (Australian digitised papers)
http://trove.nla.gov.au/newspaper/Even when there are lists in the newspapers, you may find that your research will not 'join the dots'. I explain. I have family who were born NSW, and who moved back and forth to Auckland, NZ many times during the decade before WWI. I have the family's private papers, giving me all the details. But when I attempt to validate the trips, even knowing the date and name of the ship, it is not possible. Sometimes I read Mr and Mrs Abc and infant journey to NZ, but the return journey does NOT include the infant. So you need to be careful with the research and flexible with the interpretation.
Cheers, JM