When she was put in the Special Care Baby Unit she started seizing and doctors diagnosed her with refractory seizure disorder, giving her 24 hours to live.
Six years on, Zoe is dependent on several pharmaceutical drugs which Ms Jeffries said made her drowsy and unresponsive.
"It's the ups and downs that make it hard, you can only live each day as it comes and you don't know if it's going to be a good day or a bad day."
Ms Jeffries is one of thousands of Kiwis calling for clinical trials of medicinal cannabis to help children with life threatening diseases.
Suffering from as many as 100 seizures a day, Zoe is constantly exhausted.
"The seizures are such a huge strain on her tiny body which is why she is always tired."
Ms Jeffries said people needed to stop looking at cannabis as a drug used to "get high".
"All I'm asking is for the chance to give my daughter a better life. Using cannabis oil could mean she smiles more or could point to something, it has nothing to do with getting high.
"Being able to smile may seem like a small difference, but it will be huge for her and our family."
She said she believed cannabis oil was a natural product and studies had convinced her it was successful in treating a range of illnesses.
"There have been many studies done around the world ... you generally see an improvement in people's lives."
Ms Jeffries' Facebook page 'Mothers of medicinal cannabis NZ' has more than 700 members and hundreds of messages in support since it was started two months ago.
"The Facebook page has been growing every day and it is mind-blowing the amount of support I have received."
Ms Jeffries said New Zealand would be the perfect place to legalise medicinal cannabis oil.
"New Zealand has historically led the way in so many important issues and this should be one of them."
Despite the ongoing struggle, Ms Jeffries is hopeful the government will "wake up and want to get with it".
"In the past it feels like the Government has deliberately turned a blind eye to the issue but there is definitely pressure building and they will have to take notice sooner or later."
Rotorua MP Todd McClay said he had great sympathy for Ms Jeffries and Zoe.
He said there were medicines which contained cannabis extracts available in New Zealand which had undergone full clinical trials to prove their efficacy and safety and which could be prescribed by medical professionals for therapeutic purposes - with ministerial approval.
"Recently, Parliament's Health Select Committee recommended that the New Zealand medicines agency Pharmac continue to assess whether there was positive evidence from countries that subsidise medicinal cannabis as to whether it provides a useful option for managing chronic pain, particularly with terminally ill patients."
Mr McClay said that, while he was not aware of any clinical trials or evidence presented in New Zealand to support the claims of cannabis or cannabis oil as a medical treatment, he was willing to meet with Ms Jeffries to talk about any proven treatment that might help Zoe.
