Obviously a novel is a work of prose (Or at least, the one I talk about is), but what I wish to convey in the sentence above is that the novel's language is dull and commonplace, and does not contain any literary or sophisticated words/register. Is it logically correct to say so, or should I replace the word "prosaic" with something else?
It is logically correct, but your explanation of what you mean by "prosaic" is more specific, accurate and complete (though also perhaps more prosaic).
Prosaic says what it means, so it's the difference between:
"having the style or diction of prose; lacking poetic beauty" and/or "commonplace; unromantic"
"dull and commonplace, and does not contain any literary or sophisticated words/register"
Which as you can see, are somewhat different things. Depending on how important that distinction is to you, you can choose. Personally, I'd rather read your more detailed elaboration than wonder what you mean by "prosaic" in that case.