Valerie Harper -- I'm 'Dancing with the Stars' Despite Terminal Brain Cancer

Valerie Harper -- whom doctors gave three months to live back in March due to her terminal brain cancer -- hasn't just defied medicine by staying alive ... she's signed on to "Dancing with the Stars."

As we reported, 74-year-old Harper -- famous for playing the role of Rhoda on "The Mary Tyler Moore Show" -- announced she had been diagnosed with leptomeningeal carcinomatosis, a rare form of cancer in which cancer cells spread into the membrane surrounding the brain.

Doctors gave her roughly until June to live ... but it's already August, and we've learned she's doing so well she is set to appear on the upcoming season of "Dancing," an extremely physically-demanding reality show.

We're told Valerie and her partner Tristan have already been practicing for two days, and she's surprisingly good. Our sources say she's completely self-sufficient and doesn't need any special assistance ... at least so far.

TMZ broke the story ... Leah Remini will also be on the next season, as well as Snooki, Elizabeth Berkley, Amber Riley from "Glee," and Christina Milian.