Ciara was diagnosed with a high-grade glioma, which doctors reportedly said couldn't be removed because of the risks of brain damage, stroke or death.
"I think we are very fortunate to have him in this country, that's for sure, because no one else would touch her," Nelson told Nine News.
"No one would touch her with a 10-foot pole and we are just lucky that he took a gamble and was able to do it."
Despite the relief that surgery went well, Ciara still has a four-week to make sure the tumour was completely removed.
"She is getting stronger every day. She is still very tired and it is going to take a while. There is a little bit of disturbance to her vision, but we are hoping that it's only temporary," Nelson said.
Nelson, a mother-of-three, first thought Ciara suffered a concussion when she started vomiting after a fall during a netball game in May, 2016.
But in a horrific discovery, Ciara had a lesion on her brain and her GP referred her to Monash Medical Centre in Victoria.
A follow-up MRI found Ciara's tumour was high grade.
"They admitted her so quickly. By the afternoon, the neurosurgeon told us she had a glioma in her brain," Nelson said.
A year of medical appointments, scans and disappointments followed as doctors said surgery was too risky for Ciara.
As an MP it is sometimes difficult, but then sometimes we can use this role for the best outcomes ever.
30k in 30 Days...
Posted by Brad Battin MP on Wednesday, 14 March 2018
Knowing the ordeal ahead of them, Nelson set up a Go Fund Me page to raise money for the cause, which since December 2016 has garnered more than $130,000.
Any money raised that is not used for Ciara's treatment will be donated to support other families who have children with brain tumours.