"I'm putting forward the case on behalf of all Australians," she told ABC News on Tuesday.
"They have had enough with the politics of this and they want this place, the parliament, to get on with the job."
The Warringah MP nabbed the seat from former prime minister Tony Abbott on a platform focused on climate action.
Mr Abbott abolished the climate commission, created by Labor, two years into its existence when he became prime minister in 2013.
More than 20,000 people have so far supported Ms Steggall's bill online through a dedicated website, which assists them to contact their local MP about supporting the legislation.
Bills introduced by independent MPs don't usually progress through parliament as they're pushed to the bottom of the priority list by the government.
Labor's energy spokesman Mark Butler said while the opposition welcomed efforts to progress climate action, the government would have to allow debate on the bill in parliament.
"When Labor moved a motion to declare a climate emergency last October, Scott Morrison wouldn't allow the question to be debated at all," he said.
"Scott Morrison and his divided government have never taken action on climate change seriously."
A fresh round of infighting has broken out within the coalition over climate and energy after the government promised $4 million for a feasibility study into a coal-fired power station in Queensland.
The Nationals are cheerleading for the project but moderate Liberals want greater climate action, particularly in the face of public pressure after the devastating bushfire season.
Ms Steggall's bill has piqued the interest of Australia's industry and business sector, who have been calling for certainty on energy and climate policy.
Clean Energy Council chief Kane Thornton hopes the bill brings an end to "political squabbling" on climate action and helps renewable energy investments bounce back.
"With renewable energy responsible for just over 20 per cent of Australia's total electricity generation, there is a significant opportunity for the industry to expand its role in combating the effects of climate change."