I agree with Bill. I think your beard looks good and I see nothing wrong with the colour which I would not describe as "red" but rather more auburn, and I too cannot imagine why you should want to dye it. And remember, should you actually decide to dye it, given that beards grow quite quickly you will have to repeat the process at regular intervals in order to maintain the look.

Keep growing. Stay bearded (and undyed)!

wulff