Police said a 58-year-old man had been charged with dangerous operation of a motor vehicle causing grievous bodily harm with callous disregard. He is due to appear in Brisbane Magistrates Court on October 25.
Messages of support were posted on social media yesterday wishing Stevenson a speedy recovery.
Networking group Venn posted a photo of the "bubbly Brisbane businesswoman", offering thoughts and prayers to her family.
"It is with great sadness that we find out today that the woman involved in the hit-and-run incident at Bowen Hills yesterday is one of our members, and a dear colleague and friend," the post read.
"Such a horrific act to have occurred to such a spirited, loving and incredible soul. We understand that Iuli has undergone emergency surgery and her condition remains critical. Our thoughts and prayers are with Iuli and her family during this difficult time."
Bystanders at the scene rushed to Stevenson's aid after the accident.
Her friends say her positive attitude and fighting spirit will help in her recovery.
"She's such a bright and positive person, she brings such an energy to any room she walks into. It's just such a tragic thing that's happened," friend Kate Dean told Australian media.