Ms Palszczuk says she hasn't made up her own mind on the issue, but understands the pain people feel watching loved ones struggling with terminal illness, having seen her own grandfather suffer from cancer.
"I think anyone who watches such a tragedy unfold, especially when it's someone so close and such a loved one, is, of course, going to be moved by that," the premier told reporters in Roma.
She says her Labor government, which was re-elected in November, won't consider the issue during the first year of its term, but she will consider launching an inquiry into the issue "down the track".
The government will also be looking closely at the implementation of the Victorian laws.
"I want to see how that operates first before we take any other steps."
Mr Muir says the trust will advocate for MPs on all sides to address the issue, saying current laws leave people with the choice of enduring intolerable suffering or breaking the law to end their life.
"We should not continue to force people to take things into their own hands because of a lack of law reform that would give them a lawful and dignified death in a strictly regulated environment," he said.
Opposition Leader Deb Frecklington said it was "nice to hear" the premier had no plans to change the law.
"This is a very emotive issue and, personally, my position is that the laws don't need to change," Ms Frecklington said in Brisbane.
Queensland MPs will take their seats in parliament on February 13 for the first time since last year's election.