On his 31st birthday, Ryan Geoffrey Cole allegedly shot dead a neighbour in front of two girls.
Police say he then fired the gun he had obtained illegally at a good Samaritan.
Queensland MPs are now being asked to back a bill before parliament that will strengthen gun laws after the north Queensland tragedy.
Police are yet to find the weapon or a motive after Cole allegedly killed Natalie Frahm outside her Mackay home on Wednesday.
Cole is accused of fatally shooting Ms Frahm as she sat in a car preparing to leave for a sporting activity, with two girls - aged 11 and 12 - in the back seat.
Cole then allegedly shot James McGill who came to 34-year-old Ms Frahm's aid after the girls escaped the vehicle and raised the alarm.
Police are investigating how Cole allegedly obtained the firearm after having a weapons licence revoked three years ago.
"At the end of the day this person had firearms illegally," Police Minister Mark Ryan told reporters on Friday.
He called on MPs to back a bill that would allow warrantless searches by police for illegal weapons on "high-risk" individuals.
The bill - introduced to parliament in May and set to be debated later this year - addresses the "increasing risk of firearm-related offences".
Reported offences involving firearms in Queensland rose by 30 per cent in the past decade, with more than 3000 in 2023.
Premier Steven Miles said he would consider any changes to keep the community safe.
"It's not the case that changing the regulation of firearms wouldn't necessarily have prevented this awful murder," he said on Friday.
"But we do have changes to the firearm laws before the parliament right now.
"If there are any changes required to keep the community safe of course we'll consider that."
Tributes poured in for Ms Frahm after the "horrific tragedy".
"I don't think there's a single person in Queensland whose heart doesn't break for Natalie and her family and friends and this community," Mr Ryan said.
Ms Frahm was remembered as a kind person and keen athlete, with her local Thai boxing club among many paying tribute.
"Natalie always had the most infectious smile, always helping where ever she could, making close friends," the club posted on Facebook.
The club set up a GoFundMe fundraiser for the two girls, with more than $15,000 pledged on Friday.
Ms Frahm's parents flew in from Mount Isa as the shocked Mackay community rallied around the girls.
"The community is reeling. This is the sort of thing that just doesn't happen in Mackay," mayor Greg Williamson told AAP.
"The two young girls who were in the back of the car and ran off to get help are going to live with this for the rest of their lives."
He hailed the bravery of the girls as well as Mr McGill.
The 66-year-old was visiting his elderly mother nearby when he answered the girls' call for help.
Mr McGill was allegedly shot by Cole, suffering hand and chest injuries but is in a stable condition in hospital following surgery.
"It's a typical Australian reaction I think - you go in and help," Mr Williamson said of Mr McGill's heroics.
Cole sparked an emergency lockdown and police manhunt before being charged with murder and attempted murder and has been remanded in custody.
