In short, I don't think there is a global answer for this, and there can be no real consensus - the answer would lie in the specific details and circumstances of the person (and family) in question and may still be open to interpretation.
I am not fluent in Australian history, but was Victoria a colony of Britain at the time? If so, some may not consider this to be migration since they were under the same government and the colony was already established. That may be viewed as akin to moving from one US State to another. However, others may see moving to a colony on another continent as migration since there was a complete upheaval of the normal lifestyle and comforts to expand in a new place - whether or not it fell under the management of a singular government.
As for the specific profile in question, there is not much information to go by right now, so I think it will just come down to a judgement call based on the facts available. If you consider the surviving family to have migrated, then the infant son, even though he did not reach the shore alive, would have also been under the same migration umbrella in my opinion. The cause of death may have even been due to the migration - so I it is important to note on the profile as you have done.