Woodside is proposing to develop the Scarborough gas field through offshore facilities connected by a 430km pipeline to its Pluto LNG onshore plant.
The $16 billion project would also include expansion of the Pluto facility.
It is currently awaiting approval from WA Environment Minister Amber-Jade Sanderson, having secured the green light from state and federal environmental agencies.
A decision is believed to be imminent and would include consideration of an updated Pluto greenhouse gas abatement plan.
Woodside is aiming to achieve net zero direct emissions by 2050 or sooner and has set targets of 15 per cent reduction by 2025 and 30 per cent by 2030.
A spokesperson on Thursday said the project had been subject to extensive review and would deliver one of the lowest-carbon LNG sources in Australia.
The CCWA/TAI report claims approvals were granted without sufficient consideration of the potential damage to heritage-listed Murujuga rock art on the Burrup Peninsula.
It said the project would "significantly increase" the duration of time that the ancient art is exposed to noxious emissions, which could weather the petroglyphs.
Former WA premier and National Heritage Council chair Carmen Lawrence compared the potential damage to Rio Tinto's destruction of the Juukan Gorge rock shelters.
"We have seen from what happened at Juukan Gorge that our community expects better when it comes to protection of our priceless and irreplaceable Aboriginal heritage," she said.
Woodside said protecting the rock art was a "critical issue" for all stakeholders.
"Our collaborative relationships with traditional owners, governments and community stakeholders are essential in our ability to effectively manage heritage," a spokesperson said.
"We also apply significant effort to monitor and manage our environmental impacts, consistent with industry standard air emissions management practices, our internal management system, regulations and environmental licence requirements."
The Scarborough project forms part of Woodside's enormous proposed $43 billion Burrup Hup mega-project, which would also include development of the Browse gas field.
CCWA last year launched a Supreme Court challenge against Woodside and the state government, claiming environmental approvals granted for the project may breach the Environmental Protection Act.
The challenge remains before the court.
A final investment decision from Woodside and its partner BHP is expected later this year.