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 that her condition remains critical.
"Our thoughts and prayers are with Iuli and her family during this difficult time."
Other people commented on posts of Stevenson's injury, claiming to have known the 27-year-old.
"I work with her company. Very lovely girl," one person wrote.
"The poor girl. We had mutual friends growing up in NZ and she's such a beautiful girl. I hope she recovers," read another.
A GoFundMe page has been started to help her and her family as she remains in hospital.
Police inquiries continue.