What could it have been. An epidemic, influenza perhaps? I wasn't able to pin-point a major Wellington pandemic which coincided with those dates. There was an influenza outbreak in 1918 - the spanish flu - but no mention of anything earlier in the national library. I did however come across a letter to the editor of the Wellington Independent in 1873 which described conditions in Wellington at the time, and typhoid fever was rife. I have included some of the letter below - the sanitary conditions as described paint a vivid picture of the conditions which could easily have brought about the children's deaths (and with no penicillin or antibiotics to fall back on).
Wellington Independent, Volume XXVIII, Issue 3776, THURSDAY, 10th APRIL 1873, Page 2
It is almost twelve months since that the City Council went so far as to recognise that drainage was a necessary thing, yet the city remains at the present moment as undrained as ever. There has never been exemplified any realization of the necessity for establishing a thorough sanitary system in Wellington. There has been much talk about it, but nothing has been done, although every week deaths occur which are beyond doubt traceable to the absence of those precautions which science has proved to be effectual as against many of the fatal epidemics which periodically attack centres of population.
The City Council may urge in extenuation that they could not provide a thorough system of drainage until the waterworks are completed, and this may be true. But there are many directions in which sanitary action could be taken, but which have been criminally neglected. It is sufficient for anyone to walk along any of the principal thoroughfares of the city to be able to understand the origin of the sickness which is now so prevalent. Every drain grating is simply a channel of miasma. After sundown, when evaporation is greatest, the foul and fetid fumes which are discharged from every opening to the drains is simply overpowering. Surely the least that the City Council could do is to provide traps so as to prevent the noxious effluvium from contaminating the outer air.
It is well known that at this moment the worst form of typhoid fever is prevalent in the city. Several lives have been lost from this cause already, and there is a strong probability that many others will follow. Now, if there is one thing above another which modern science has been able to establish it is that zymotic diseases, such as typhus fever and typhoid disorders generally, are entirely traceable to the neglect of sanitary precautions. If the City Council cannot yet undertake a thorough system of drainage, they can, at least, mitigate the evils consequent upon the absence of such a system. They can and ought to take measures for ensuring the regular and constant clearance of the closets within the city. This, of itself, would be a very considerable step, for anyone who knows anything about the average state of the back premises of the city knows that it is simply disgraceful. In various parts of the town are to be seen filthy streams of pollution reeking in the sun and breeding disease around them.
What is required and and what should be done is that a regular house-to-house inspection should be made ; the City Council should establish means for the 1 regular clearance of outhouses, and we are sure that the ratepayers would gladly pay the cost. If something of the kind, is not done speedily the metropolis of the colony will become a place to be avoided.