Bindi won the 21st season of the show at just 17, alongside dance partner Derek Hough.
The pair received a perfect score of 30 for their last performance on the show.
Now, a decade later, she hopes Robert, 21, will follow in her footsteps and take home the final prize.
“He is going to shine though, and I know in my heart he is going to make it far because he is such a fantastic human being,” she said of her brother.
Bindi urged her followers to support her younger sibling by following him on social media.
She said she would continue to give updates about the family’s time in the States during their stay.
Bindi and Robert’s mother, Terri, has also taken a break from wildlife conservation to support her son.
Australia Zoo, which the family continue to own and operate, is the legacy of family patriarch and Australian television personality, Steve Irwin.
The “Crocodile Hunter” tragically died in 2006 after being stung by a stingray, when Bindi was 8 and Robert just 2.
Bindi dedicated several of her Dancing with the Stars performances to her late father, including a safari-themed dance to Crocodile Rock.