After extensive exploratory and reconstructive surgery, he is in a stable condition and due to be released home.
His wee boy Averroes suffered minor injuries, including a gunshot wound to the leg and backside.
He was discharged from hospital six days after the shooting.
The family has asked for privacy.
However, the Herald has been allowed to publish details of Alta's public Facebook posts.
"This has been a difficult time for us and so many others," she wrote.
"I am so thankful to have my husband and son still alive and that we have received an outpouring of support from so many people around the world."
Last week, the family met Prime Minister Jacinda Ardern.
Alta said Ardern was "exactly as we expected her to be: full of grace, compassion, and empathy, coupled with a willingness to tackle the unmet needs of individuals and the entire nation".
"Once again, we are grateful for the endless stream of support we have received. The medical care has been top-notch and we will be forever grateful to each person who has had any hand in easing the difficulties of this situation," Alta said.
A Givealittle page set up for the family said the toddler was traumatised from the tragic event.
The page explained that the family recently relocated from Indonesia, which is Syah's homeland.
He was described as a talented, hard-working artist, while Alta is an American who has lived in Indonesia for many years and had a dream to settle in New Zealand with her family.