It is humorous. The writer is describing a dog baying or howling in a very dignified way, as if it were a trained singer or musician.
I have not heard the word "bell throat" applied to a singer. It is the description of a brass instrument, the way a part of it tapers. I think the idea is that the dog is producing a very rich, full, loud sound.
"Range" means that the dog can produce very low and very high notes--in other words, a very irritating sound, like a siren. "Control" I think means "breath control," meaning that the dog can keep making that loud sound continuously for a long time, before having to take a breath.