You are right, I think he looks a little young for brumation. You say he's lethargic, won't eat or drink, and has runny stools? Have you fed him anything out of the ordinary lately? I fed my beardie a grasshopper as a treat for the first time and she had these symptoms. I took her to the vet and they said that grasshoppers hurt her stomach (some dragons are okay with them). I had to give her medicine for the rest of the week. Could it be that?
Bearded dragons can also get parasites. It may not be your fault, but it is very serious. I highly recommend that you take your bearded dragon to the vet very soon. Hope this helped! If you have any questions, feel free to ask.