While my degree in Cultural Anthropology focused on the Plateau Indians of the NW, I did do a little bit of research on the Lakota Indians (mostly by researching various trade routes). Now I know Deities & Demigods cites Dakota, but Lakota is very closely related to Dakota -- basically different dialects of the same language.
By doing a cursory glance through two books, Beginning Lakhota (from the University of Colorado) and Lakota Myth (by Elaine A. Jahner) I noticed a couple of things. First, the letter "q" is never used. "K" is always used for the velar sound in words. Now I know that's a matter of semantics (since both "q" and "k" make the same sound) but the fact that when writing various words and they never use the letter "q", well, that kinda says something.
Second, I never came across the double vowels "aa". Again, this is semantics as, linguistically, there are various ligatures used for this long vowel sound.
So, I took the word Qagwaaz, and reconstructed it as Kagwaaz or Kagwaz (technically, I think it would be "Kagwæz" but its been years since I took Linguistics, so I can't remember). Either way, I couldn't find anything that matched it in either book.
Of course, in Lakota Myth, the character that gets mentioned a lot is Iktomi - a trickster. And many of the other characters have been anglicized: Buffalo Woman, Stone Boy, etc. I didn't really come across anybody that was "a powerful warrior who wanders the plains alone, capturing wild horses and hunting buffalo solely for the sport of it." But thats not saying the story does not exist. Every culture has tons of folk stories and myths. And many of them become forgotten in various books
So my best guess, and again this is just from a cursory review, I think Votan is right -- somebody just made him up. Maybe he was somebody's D&D character? Like many people, I tried to find the name through the internet and its association to American Indian lore. But like everybody else, it just kept pointing me back to the Deities and Demigods book.
It would be nice if somebody had a relationship with one of the authors of the book -- James M. Ward or Robert J. Kuntz. Maybe they could ask one of them where they got Qagwaaz from?