She is now receiving treatment in the hospital's burn ward.
Hundreds of Facebook users said they were heartbroken by the footage.
"That is just heartbreaking. Thank you for taking care of the injured wildlife, it must be a hard thing to witness all the injuries of the animals coming in," one user said.
"Such compassion and gentleness in the rescuer's care for this clearly injured and hurting koala. Thank you and more thanks to you all for bringing Kate to the Koala Hospital. May she recover fully and be relieved of her pain," another wrote.
One added: "The poor darling. Breaks my heart just thinking about what she's been through. Thank you to all those helping our wildlife during these tough times."
It is believed more than 350 koalas may have perished in the recent fires across NSW.
A GoFundMe page has been set up to help the Port Macquarie Koala Hospital nurse the koala's impacted by the fires back to health.
The campaign has almost reached $500,000 in donations.
"The Port Macquarie Koala Hospital is an animal welfare, scientific research and education facility that will send out and conduct search and rescue exercises in the hope of finding surviving koalas," the page reads.
"Any surviving koalas will be brought into the Port Macquarie Koala Hospital for assessment and treatment.
"One way to help surviving koalas and other wildlife is to provide access to water to reduce further deaths from dehydration.
"The Port Macquarie Koala Hospital would like to raise money to purchase and distribute automatic drinking stations which will assist in helping koala and wildlife survival."
The money raised will be used to distribute the drinking stations throughout the fire affected regions across the state.
"With rising temperatures and increasingly dry conditions worsening across the State, access to water is essential for survival," the page read.
"Please help to enable the Port Macquarie Koala Hospital to undertake this project. All assistance is greatly appreciated."
Taronga Zoo made another call for donations to the hospital this afternoon, releasing a statement calling for help. The zoo, a partner of the hospital, has sent emergency relief funds to the facility, and said its two wildlife hospitals and wildlife health teams were on standby to offer emergency assistance to "the defenceless wildlife fallen victim to the earliest and worst bushfire season NSW has ever faced".
"Pressures on the Koala were already compounding – habitat loss and land degradation, disease, highly fragmented populations, droughts and heatwaves, climate change, predation by non-native species, and urban growth," Taronga director of welfare and conservation Nick Boyle said.
"And now this. It's difficult to digest but there's only one thing to do and that's to step quickly into action.
"Once these bushfires pass, there will still be a crisis for koalas. The next couple of years will be more important than ever for the long-term future of koalas."