The international student, living in Toowong, had spent two weeks in isolation in Dubai before flying to Brisbane.
Health authorities believe the man was infected while in isolation in Dubai.
Premier Annastacia Palaszczuk said she had “some concerns” about the veracity of overseas isolation, but it was a matter for the federal government to examine any quarantine loopholes.
Fifteen staff at Brisbane’s Mater Private Hospital were placed in quarantine after the student inadvertently exposed emergency department staff to the virus.
The Queensland government passed laws in January granting emergency powers to Dr Young that allow her to order a person to be detained under quarantine against their will and can prevent people from going to certain locations.
She can use reasonable force to compel an individual when a direction is not followed, which can include forcing someone to be medically tested against their will.
Dr Young said she had not needed to invoke those emergency powers as about 2700 Queensland residents have done a “fantastic” job of self-isolating since the outbreak.
“We give them information so they have it in writing,” she said.
“They have all complied so it has been an absolutely brilliant response and I have no concerns going forward.
“Queenslanders are really, really perceptive to that advice about how to protect other Queenslanders.”
Dr Young said planning was under way to supplement frontline health staff if more were exposed.
In an effort to prepare for an outbreak of the virus in Queensland, a disaster scenario meeting was held by the Premier on Friday morning.
“I know there are mums and dads and students out there who are worried and my message is, do not panic,” Ms Palaszczuk said.
“We are making sure that we are ready to deal with any potential outbreaks but there is no need to panic at this stage. We have everything in place that needs to be in place.”
Dr Young said as of noon on Friday, Queensland had 13 confirmed cases of coronavirus.
“Every single one of those cases, we know how they contracted it,” she said.
– with Stuart Layt
Lydia Lynch is a reporter for the Brisbane Times