Families of the children and women in the camp have written to Prime Minister Scott Morrison to beg for faster help, amid fears the scorching Syrian summer will exacerbate the injuries and illnesses the children are already suffering in the sprawling camp, where 73,000 detainees are living in squalid conditions.

The families have vowed to take responsibility for helping reintegrate children and family members who are brought home.

At least 22 of the children are under the age of 10, according to a comprehensive list compiled by the Australian branch of international aid group Save the Children and seen by The Sydney Morning Herald and The Age.

They have a range of injuries and illnesses, including shrapnel wounds, ear damage from bomb blasts, broken teeth, rickets, malnourishment and post-traumatic stress disorder, Save the Children and the families say.

The families say other camp detainees have threatened the lives of Australian women and children.

The six-year-old girl, named only as "Rand", has been "shot in the neck, resulting in nerve damage in her shoulder and arm", which she is "unable to move", the aid group's notes state.

Originally from Victoria, the girl was hit by the bullet - which had previously passed through someone else - while fleeing from the town of Baghouz where IS made its final stand.

A boy aged less than one year, born to Australians who were Islamic State members, is described as "premature and extremely underweight". There is a seven-year-old who is suffering "uncontrollable shaking" fits and seizures, and a two-year-old with "excessive diarrhoea" stemming from a bowel condition.

Australian detainees at the al-Hawl Kurdish-run camp, where daytime temperatures are already reaching the high 30s, include "some heavily pregnant women, children with disabilities and mothers and children suffering from untreated shrapnel wounds", the families wrote in their letter to Mr Morrison.

"We are part of the fabric of our society and we call on you to act urgently and humanely," their letter states. "We are all willing to work with the government. When they do return, we will help them pick up the pieces of their lives and rehabilitate them so other citizens, the country and you will be proud of them."

The letter was sent via Save the Children on May 6. Mr Morrison replied on May 10 and said he was "deeply concerned" about the children but warned that "swift results cannot be guaranteed" in getting them to safety.

The Morrison government has said unaccompanied minors - whose parents have been killed fighting for the terrorist group's former "caliphate" - are the priority, though these are understood to make up only a small proportion of the group.

Reports on Thursday indicated three orphaned children from the same Australian family of Bosnian heritage would be among the first repatriated. The Herald and The Age have been told steady work has been done on the problem but some obstacles remain.

Mat Tinkler, director of international programs for Save the Children, which is working in al-Hawl and other camps, said "children are dying from hypothermia, pneumonia, dehydration or complications from malnutrition".

"Children have shrapnel wounds which aren't being treated and our staff are seeing severe symptoms of post-traumatic stress disorder in very young children," he said.

Three children and two grandchildren of notorious Islamic State convert Khaled Sharrouf and his wife Tara Nettleton are in al-Hawl camp.

The eldest daughter, Zaynab Sharrouf, is heavily pregnant with her third child.