The champion swimmer published a picture of herself and Hannah, wearing an Australian team shirt, with a big smile to her social media.
"Twelve-year-old Hannah lost her leg to a shark attack only three weeks ago while holidaying in the Whitsundays," Cole wrote.
"Today she jumped in a wheelchair for the first time and I couldn't even keep up with her. She's going to be great."
Cole, who is a six-time Paralympic champion, lost her right leg to a rare cancer as a three year-old.
Rescuers marvelled at Hannah's bravery as she smiled and gave them a thumbs-up as she was loaded into a helicopter after being stabilised on the island beach.
She was accompanied by her engineer father, David, as her mother, who was in New Zealand at the time, rushed back to the country.
Barwick, 46, underwent an 18-hour surgery to save her right leg.
She flew home to Tasmania last week to continue her treatment in Hobart.
Six large tiger sharks were caught and killed on baited drumlines deployed at the island after the attacks.