A Givealittle fundraiser, set up by family friend Tania Wright, said their "beloved" dog Sumo died in the fire that "destroyed" the Ashton St house.
Within three hours the page had raised about $1300 of its $10,000 goal.
Family home destroyed - Givealittle
Their other dog, Nala, and a cat survived.
Ms Wright said "what should have been a pleasant afternoon with her babies turned into a nightmare that nobody should experience".
"Now there are the costs of starting over for four children and herself, plus vet bills and so on."
She said funds raised would be used to replace household items, clothing, food and more.
The family was not home when the fire broke out.
A Fire and Emergency New Zealand spokesman said five appliances from Mosgiel, Outram, Roslyn and Lookout Point were sent to the blaze at 2.45pm.
By 4pm, the blaze was extinguished.
A fire investigator is working to determine the cause.
