I just found a pamphlet from NSW State Records on Shipping and Arrival Records (dated March 2013 so reasonably up to date). It indicates that the practice of not naming unassisted , i.e. paid for, passengers was "prior to 1854" . However, most of their indexes - and those produced by others such as Pastkeys etc. seem to end around then - though I haven't checked NSWSR website to get an update on that date.
They say [as at 03/2013 anyway] :
Passenger lists are arranged chronologically by arrival of the ship. As there are no comprehensive indexes to passengers arriving after 1855, and if the name of the ship and the exact year of arrival are unknown, researchers will need to try to determine the date of arrival from other sources.These comments are for NSW arrivals only, of course. They could have come in via Melbourne or Queensland or Western Australia. So when you look at TROVE, think of Victorian & Queensland & WA papers, not just the Sydney ones. Names of arrivals by the latest ship were often published in the papers of the day, presumably so any relatives could know they had arrived.
BTW I think you will find that the name of the ship the second lot of children came on is
Murrumbidgee - double e at the end. the Murrumbidgee is a rural area in southern NSW. When I googled the spelling you gave, it only gave me Murrumbidgee.
Dawn M
