The baby, seriously injured when his grandmother, Julie Ferne, died after falling three storeys in Vietnam while carrying him, is well enough for his father to return to New Zealand for Ms Ferne's funeral tomorrow.
Julie Ferne, 68, died last month after toppling over a railing and falling with Carter in her arms at her son's home in Ho Chi Minh City.
Baby Carter Preston was four-days-old at the time of the accident, and three weeks on is doing everything that a baby of his age does.
"There's actually reasonable hope he might well recover," Carter's uncle Stefan Preston said today.
Carter's mother, Chau, was now able to stay at the hospital with Carter and she could see him for half an hour every three hours.
She was also able to feed him.
Carter's improvement meant his father, Phil, could return to New Zealand for Ms Ferne's funeral in Auckland tomorrow.
Mr Preston described the funeral as a celebration of her life
"The casket's been painted by a whole lot of artists and all her grandchildren. There's a lovely video, we've planned a really amazing service and we're just looking forward to celebrating her life, together as a family."
There was a lot of meaning behind the service.
"Being ... an artist she would have been absolutely blown away with the funeral, there's no doubt about it."
A trust fund set up in Ms Ferne's name to buy hospital equipment in Vietnam has so far managed to raise about $50,000.
Mr Preston said following the funeral he and his two brothers would work together to strategise how to make the most of the fund.
"It's incredibly gratifying for us that we were able to do something like this in our mother's name. We've been absolutely blown away with what we've been able to do."
People wishing to donate to the Julie Ferne Memorial Trust can deposit funds in ASB account 12-3198-0065427-00.