Well sure- Owls sleep during the daytime, so "Singing as dawn shines above," makes sense- it's a lullabye before going to sleep. I'm for "dawn," and that's how I first heard it. My older sister Kitty was a girl scout leader- she probably brought it to us from scout camp, in the early 1930s. So, we're all pretty well agreed on the source. Our chorus went,

Te-coura coo-ah, coo-ah, coo-ah (imitates the owl's call)
Te-coura coo-ah, coo-ah, coo-ah
Te-coura coo-ah, coo-ah, coo-ah
That I may fly to my love, etc.

No Joe, I never recorded this, nor published it, just sang it-to many many kids, and for my own pleasure.   Jean