Linley Anyos went to a home on Trees Road, Tallebudgera, in Queensland's Gold Coast about midday on Wednesday when she was shot in the back.
The 33-year-old was sitting in the passenger seat of a car and police suspect the gunshot came from inside the vehicle and went through the seat.
"The victim remains in a critical condition, she's classified as serious but stable," Detective Inspector Mark Mooney told reporters on Monday.
"The doctors will be looking to bring her out of sedation today, which is a really critical stage for her.
"There's obviously an opportunity that she could go into shock and still pass away from her injuries. Her injuries she sustained are significant, and they'll be life-altering."
Ms Anyos' father Brian said his daughter is in a "very bad way" but is "fighting like a beast".
"This is friggin tough on us and ... please respect our wishes, knowing full well we will pass on every single message for Linley as they come through," he wrote on social media.
Police are now appealing for public information and dashcam footage of a white Hino tow truck that they believe left the scene immediately after the shooting.
Det Insp Mooney said the tow truck drove around the Tallebudgera area before returning to Nerang after the incident.
Investigators are still piecing together the full puzzle after taking more than 10 witness statements.
Police executed a search warrant at a Southport address on Friday looking for a person of interest.
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