I wonder if Prairie Dawn was named before The Muppet Music Album. It would be kind of funny if for that album, the name was needed for the contestant in What's My Letter? and then when it was made into a video sketch that puppet was used, due to a similar voice, and the name stuck (then again, Betty Lou didn't continue being called Lucy Jones, then name given to her in Pick Your Pet).
For the longest time when I got that album (well, the rerelease titled Sing the Alphabet) I thought it was strange that the little girls performed by Fran Brill in The Question Song and Just Because were different from Prairie Dawn. And those two girls seemed to have Prairie's current personality. Compare Prairie's personality in early appearances like What's My Letter? and then later appearances like The Triangle Game or the Letter of the Day sketches and there's a noticable difference.
Another big difference between Prairie and Betty is the fact that Prairie Dawn pretty much alwasy had the same performer, though it sounds like Jerry Nelson performed her in the handclapping sketch from episode 536, while until the 1990s Betty Lou was performed by whoever was available.