On Friday, the page had generated $1,891 -- with donations coming from as far as The Netherlands.
With more donations than expected, Joshua and his partner Danielle Bolt will put any leftover money towards education for Noa, who has Down syndrome.
"I thought I'd get a maybe couple of hundred dollars.
"It's amazing how many people have come on board -- I've had donations from absolute strangers.
"Obviously, our story has touched people."
Joshua and Danielle were shocked when a scan found their unborn child had Down's syndrome.
While several close friends advised terminating the pregnancy, the parents-to-be were undeterred.
"The experiences I'd had with Down's syndrome weren't nice -- my mum worked with a boy who was very aggressive.
"But Danielle opened my eyes - she had done research and watched videos on children with Down's syndrome, and saw their potential.
"We weren't giving up on our baby -- why should we?"
A seemingly healthy Noa was born on June 30 at Wairarapa Hospital -- but her parents' worlds were rocked again when their midwife discovered Noa was breathing abnormally fast, at 97 breaths a minute. The breathing rate for a calm, newborn baby is 40 breaths per minute.
A hospital paediatrician discovered a heart murmur and called a Life Flight Ambulance.
"We were freaking out."
Danielle and Noa have since remained in Wellington Hospital, where doctors are waiting for Noa to reach 5-10kg before operating.
Meanwhile, Joshua is unable to take paid leave to visit, as he has only been in his job five months, and doesn't qualify for Government assistance.
"Givealittle was a last resort.
"It's a nightmare -- I can't see my partner, and I can't see my child."
But he is heartened by the possibility of extra funds for Noa's schooling -- and has started investigating Rudolph Steiner schools.
"They integrate children with disabilities with everyone else in the classroom.
"She shouldn't be separated; she doesn't have a disease."
Joshua knows life with a disability could be challenging for Noa -- but he is every inch the protective Dad.
"Anyone who speaks badly of my daughter will have me to deal with."
To support Joshua and Danielle, go to givealittle.co.nz/cause/noasdad.