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The tot was born prematurely with dextrocardia where the heart is on the wrong side of the body.
But Miss Pirini did not know about the extent of the rare condition when she moved her four boys to Australia in December in search of a better life.
Now her brother has set up a fund to help get Noah home.
When Noah was born in Auckland, doctors said his heart was inflamed but the condition's severity, including lung defects, was not realised.
Doctors continued to diagnose bronchiolitis until the family, including older boys Tyler, 13, Vinnie, 11, and Cadence, 2, emigrated to Australia.
"Two weeks after we got here Noah coughed up blood," Miss Pirini said.
The solo mother rushed her son to hospital where specialists identified damaged valves leading from Noah's lungs to his heart.
Noah had surgery at Mater Children's Hospital in Brisbane in January to fix the valves and widen the pulmonary veins in his lungs to let more oxygen through.
The prognosis was that he would likely need more surgery as he aged to keep the narrowed veins open.
Then two weeks ago, on Noah's first birthday, Miss Pirini was blindsided by the news that all but one of the veins had closed and there was nothing more doctors could do.
"He's only got one vein left working and they've said it's just a matter of time until that closes and that will shut down his heart," Miss Pirini said.
"There's no other surgery they can do. I asked about lung transplant but Noah will need both heart and lung transplants and he wouldn't survive the surgery."
Noah was sent home with weeks to live.
"I just cried. You just look at him and I think 'Well, what if tomorrow's the end?'.
"So I just want to get him home and spend every minute with him."
Noah was a "fighter". He needed oxygen and had not learned to crawl or sit yet on his own, but he showed no other signs of his illness, she said.
Miss Pirini, a former New Zealand Post worker who has not been able to work since arriving in Australia because of the amount of time Noah has been in hospital, said she was unaware her brother had set up the fundraiser with Givealittle until she began getting messages of support.
"My biggest concern is just getting him back on to New Zealand soil because I'm a single mum and if anything was to happen here, there's no way I'd be able to get him home."
Miss Pirini has managed to survive on family tax credits and by staying with aunts but she plans to move home permanently and faces start-up costs including a rental home, a car to get Noah to Starship hospital, furniture and schooling requirements.
So far, $3,450 had been raised and Miss Pirini, who's from the Hokianga in Northland, hoped to fly the family home on her 35th birthday on Monday.
She said that when the end came she planned to take Noah back to Pawarenga where she grew up.
• A rare congenital condition where the heart is on the right side of the chest instead of left.
• In some cases it is linked to heart and organ problems.
• Dextrocardia that affects heart function can cause breathing problems and fatigue in children.
• Treatment includes surgery and long-term antibiotics to fight respiratory illness.