NBC News says the program examines Harper's "raw and emotional journey as she battles a rare incurable disease."
Yet Dr. Jeremy Rudnick reveals that Harper's fight against terminal brain cancer has taken a hopeful turn and that the latest MRI suggests she "was pretty close to remission.""The Mary Tyler Moore Show" and later on the spinoff "Rhoda."
This season, she is competing on "Dancing With the Stars," which airs at 8 p.m. Mondays on ABC.
"I think the show will play a major part in my recovery," Harper tells In Touch. "I feel much better."
She also tells the magazine: "I prefer to live as thought this is all we have, because we could drop dead at any given moment. When life asks you to dance, you just have to dance."
On Thursday, Harper told "Today" that she took the show to highlight that so many people are living with cancer. She said she was having trouble with her knees, but she was following the motto that you have to keep moving.
"Live your life while you're alive," she urged "Today" viewers.
The Vieira special will provide looks at Harper's life with husband Tony Cacciotti and their daughter, Christina.