On Facebook, Ms Brenssell and Mr Rimene appear to be doting parents and posted regularly about their young family.
'Happy bub... you fill me with love,' the mother-of-four wrote with one of the photographs she shared online.
Mr Rimene also shows a keen interest in his children, with a snap of one of them watering in the garden set as his profile picture.
It is understood by Daily Mail Australia the couple hail from the area of Masterton, north-west of Wellington.
But they made the move to Hamilton a number of years ago, according to the Herald Sun.
Neighbours have told of the terrifying screams they heard come from Israel's home before emergency services arrived.
They told 7News they heard two screams come from the home - once at 1am and then another at 3am.
Christine Storer, who lives across the road, told the ABC she was woken up in the middle of the night after hearing a loud noise coming from the home.
'I just heard a lady's voice screaming. I didn't know what happened,' Ms Storer said.
'When I saw the blue tape [on Monday morning] I was quite scared because I knew there were some little kids over there and it does frighten you.'
The baby's death is another heavy blow to the Hamilton community who are still reeling from the death of Adelaide Crows coach Phil Walsh who hailed from the 9,000-strong town.
Other neighbours have also expressed their shock at the baby's death.
'I'm pretty disturbed that such a young child had died in the street where I live,' one man told 9News.
'It's pretty tragic. I've got a young child myself.'
- Daily Mail
