There was pure joy for the safe arrival of their daughter and still the deepest grief for their son Samuel, who had died just over a year earlier, at a day old.

"This little miracle here has been a big part of our healing process," said Dr Carroll, a marine ecologist, looking down at his daughter.

There is still no explanation for Samuel's death – a bonny boy weighing 4.38 kilos who was born at 40 weeks after a complication-free pregnancy.

After going into labour, Mrs Carroll was put on a monitor at the Canberra Hospital. Inexplicably, Samuel's heartbeat was lost without a trace. Mrs Carroll was rushed into theatre to have an emergency caesarean. Samuel was born not breathing. It would be 21 minutes before his heart started to beat again and six hours until he took his first breath with the aid of a ventilator. He had suffered severe brain damage and damage to multiple organs due to a lack of oxygen.

He died quietly in his parents' arms at the Canberra Hospital on December 1, 2013.

"The first 24 hours it was really, really dark. You look inward and think, 'What did we do wrong?'," Dr Carroll said.

"And when it was time to say goodbye to Samuel, I'd be lying if a big part of me didn't want to go with him."

What did help the couple through the most difficult of times – not only in those terrible first days but for months afterwards – was the support of their families and friends. They were also helped by the resources of SIDS and Kids ACT, which is participating in Red Nose Day on Friday.

Through SIDS and Kids, the couple accessed a bereavement counsellor and other families who had suffered the same terrible loss. The other parents, almost through an unspoken connection, knew exactly how they were feeling.

"You know when you go to those groups you can say what you want and everyone wants to hear how you're feeling. It's not like, 'Oh, here we go again'," Mrs Carroll, a policy officer, said.

The couple had made a pact in the hospital that they would not let the grief consume them and they would try for another child. SIDS and Kids helped them with a pregnancy-after-loss support group. And now that little Isobel has arrived, there is a playgroup with other families who have lost a child.

"They helped us work through the pain and grief of such a tragic loss and helped us find a glimmer of hope again," Dr Carroll said.

SIDS and Kids ACT chief executive officer Lisa Ridgley said the organisation was there to help the parents and families of children lost in early and late pregnancy, birth, infancy and childhood. There had been an 80 per cent drop in sudden infant deaths in Australia, in large part due to its safe sleeping program.

But SIDS and Kids ACT was experiencing an increase in referrals for other deaths, not least because of increased awareness through campaigns such as the world-record Christmas lights.

"It's less likely to be a SIDS case and more likely to be a death from other situations and complications," Ms Ridgley said.

Samuel's passing was described as a neonatal death, with the odds of a baby dying at full term for no apparent reason about one in 1000. The Carrolls were riddled with anxiety throughout the pregnancy with Isobel. They chose to have an elective caesarean two weeks before her due date to ensure everything went well.

They praised the staff of the Canberra Hospital who supported them throughout, including the same midwife and neonatologist who had been there for Samuel's birth.

"I remember the neonatologist put her hand on my shoulder and said, 'We're here'," Dr Carroll said of Isobel's birth.

"When they gave her to me, I was just like, 'Oh my god'," Mrs Carroll said. "We just kept looking at her, going, 'Is this our baby?'

"I remember driving home with her because it was so different to last time driving home without Samuel," Dr Carroll said. And that's when it hit: this is real. And of course we were bawling our eyes out. And a lot of moments are like that: bitter-sweet."

Mrs Carroll says Samuel is "very much a part of our family". "If we write cards to family, we put Samuel's name on it. We try to make him part of the family as much as possible and Isobel is going to grow up knowing about her big brother," she said.

Dr Carroll is adamant that "Samuel is our son, our first-born and will always be the eldest of our children".

"We want to talk about Samuel and have people talk to us about him. We don't want people to feel uncomfortable talking to us about our son, about babies, about pregnancy, because Samuel was such a special part of so many people's lives and he will never be forgotten," he said.

*For more details on Red Nose Day go to www.rednoseday.com.au. The Luton Charity Ball on Saturday is also being held in Canberra in aid of SIDs and Kids ACT, www.lutoncharityball.com.au.