Very interesting post.
I would actually think language develops from rational thought. Let us look at the blind and deaf, who lack full means of communication. They are still rational because humans are innately rational, which actually makes us very special. We appeal to logic and rationality because it simply makes sense to us. We like truth. Language is a tool that helps us discover truth. But an expansive language like English or Afrikaans is not necessary. Symbolic logics like propositional logic or mathematics have shown we can express rationality with "limited" resources.
Now this begs the question of things like body language. Suppose I wanted to represent the word water to someone that does not speak the same language as me. I could motion my hands to be drinking from a cup. Or the word bird. I could ridiculously flap my arms up and down. This is because of empirical experiences.
Now, if we were to consider the case where every individual person has different empirical experiences, ie. everyone is from a different planet and we all have different things on our planet. Even in this case, supposing we are all rational, we could work things out even if it were difficult. We are deductive. We try to figure out what is going on. We work with reason. So even if I have never seen a bird before, but you flap your arms to represent a bird, I know you are trying to represent something. Although I do not know what, I hope to eventually figure it out.
As a logician, linguistics is closely knit into my field as much as we try to do without it. Problems arise all the time from language, like Wittgenstein, Quine, etc. I think rationality and language are symbiotic and grow together, but are not wholely dependent on one another.