After tests at Wairarapa Hospital found critically low sodium levels, she was rushed to Wellington Hospital to be stabilised before being flown to Starship in Auckland a few days later.
"It was all of a sudden" said Mrs Laybourn.
"It was a complete shock to the system."
Miriam was admitted to Starship's intensive care unit just in time.
Mrs Laybourn said it took a while for doctors to diagnose Miriam with Denys Drash syndrome, a very rare genetic condition which affects the kidneys.
Those with the syndrome develop scar tissue formations throughout the glomeruli, which are the tiny blood vessels in the kidneys that filter waste from blood.
This often leads to kidney failure.
One in eight million people have the condition and Miriam was the only Kiwi who had it, said Mrs Laybourn.
For much of Miriam's early life, the family went back and forth to Starship where she was the youngest patient to undergo peritoneal dialysis, 12 hours at a time, to "clean" her blood. It was extremely hard on Miriam because the treatment made her feel sick, said Mrs Laybourn.
Eventually the Laybourns set up a "mini-hospital" at their home and were trained to carry out the dialysis themselves.
Then when Miriam was almost 2, doctors said she needed a kidney transplant.
"They didn't say it in so many words but she wouldn't have lasted long," said Mrs Laybourn.
"That was a full-on time."
Mrs Laybourn was an ideal candidate to donate but because she was pregnant with twins, Miriam's father underwent the transplant to save their daughter's life.
Mrs Laybourn said they coped thanks to three things.
"Friends, family and faith."
Their church, friends and family were a great help babysitting and bringing meals around, she said.
Starship and Ronald McDonald House were also amazing, she said.
"Starship is a really positive place for us."
Miriam still has to have monthly blood tests and regular visits to Starship to see her doctor Tonya Kara, which she likes.
"She's so brave with all the things she has to have done," said Mrs Laybourn.
Miriam features in the book Starship: Inside Our National Children's Hospital. The hospital turns 21 this year and the book documents how it came into being and what is has achieved since.