Deprived of oxygen shortly after birth, tiny May suffered extensive brain damage and seizure after seizure.

"We couldn't hold her, we couldn't touch her, we couldn't really do anything which is really hard being a mum. All you want to do is hold your bubba," Ms Napper-Ferrari said.

As she lay sedated in the neonatal unit, Ms Napper-Ferrari and her partner Chris Richardson tried to make peace with saying goodbye to their little girl.

They held a naming ceremony for her, read her stories and sang her songs, while May's three-year-old sister Aida helped to give her a bath.

But their heartbreak turned to relief as May opened her eyes the next morning.

"Everybody thought she wouldn't make it. It was quite an amazing thing to see her the next day waking up and looking around," she said.

Four weeks on, Ms Napper-Ferrari has the unexpected joy of planning a life for the little girl she thought she would lose.

After initially being fed through a gastric tube, May can now breastfeed and is settling into life at home in Chisholm in Canberra's south.

But with that joy comes the uncertainty of how the brain injury May acquired will affect her life.

"What was hard for us is we'd just come to terms with saying goodbye to our baby girl when we were set with new barriers for her disability," Ms Napper-Ferrari said.

If she makes it to her first birthday, it is likely May will be diagnosed with cerebral palsy, Ms Napper-Ferrari said.

"I never thought I would have to be dealing with how our daughter will be in the future but we've got her, and we don't know how long for so we're going to enjoy every day that we do have with her," she said.

Support has flooded in for Ms Napper-Ferrarri and Mr Richardson since they brought their baby girl home.

"My mother's group came together like a little tribe, they've been my strength," Ms Napper-Ferrarri.

Rallying the "tribe" was Annalise Skaroupka.

Ms Skaroupka, who met Ms Napper-Ferrari three years ago when they had their first children and now resides in Brisbane, has raised more than $8000 and organised an Instagram auction in May's honour.

That auction will run from 8pm on Friday and Ms Skaroupka said "heaps and heaps and heaps" of Canberra mums have worked together to pull it off.

"The whole Canberra community comes together when something like this happens which is really, really lovely," she said.

You can bid in the @amiracleformay Instagram auction from August 12 to 14. You can also support baby May by donating at: gofundme.com/amiracleformay