A 30-year-old woman allegedly murdered along with her 14-week-old infant in an alleged murder-suicide was known to a local woman's safety service provider.

The horror unfolded at an outstation 25 kilometres north of Alice Springs last week, with the alleged male perpetrator found dead at the scene.

Women's Safety Services of Central Australia chief executive Larissa Ellis told ABC radio although the provider was not actively involved in supporting the woman at the time of her death, they had done so previously.

"Historically we have had some dealings with her, but we have not anything current", she said.

"Five women and children (have been domestic violence victims) in 18 months in the Northern Territory, we do really need to be looking at what are our lessons to be learned."

WoSSCA together with The Equality Institute and Tangentyere Council's Women's Family Safety Group held a community vigil in central Alice Springs on Sunday.

Dozens of people attended the emotional tribute to the pair which was held on the lawns of the Alice Springs court.

Items such as flowers and teddy bears were placed in honour of the mother and infant, whose names have so far not been released to the public.

"A lot of people in our community are hurting over the loss of a mother and her baby", a post on WoSSCA's Facebook page read.

"Let's come together to lay a flower and leave a message of support.

"Together we say no to family violence."

In a social media post the the Tangentyere Women's Family Safety Group thanked attendees of the vigil.

"Our community has suffered a dreadful loss, but we can come together and show this mother and baby are loved, they are missed and we all want the violence to stop."

The deaths come as NT Police Minister Kate Warden called for more support from the federal government.

"We have the capability to stop this (domestic violence)", she said.

"We have the capability as a community to say no more to this, but we need to work together and we need more funding".

Domestic violence related murders are six times more likely to occur in the Northern Territory than elsewhere, with First Nations women in central Australia estimated to be 60 times more likely to be victims.

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