No, a 2-month old baby is not brumating. Dragons do most of their total growth and development during their first year of life, which is why it's imperative that they get strong UVB/UVA light and tons of live insects every single day during their first year of life. So this is why they don't brumate in the wild, let alone in captivity. Beardies in captivity don't have to brumate and many never brumate at all, ever, but definitely not as young as 2 months.
Generally when someone has only had their dragon for only a month and the dragon is only 2 months old, and then their appetites slow down/stop and they become lethargic, 99% of the time it's due to an inadequate or incorrectly mounted
UVB light, or both, and improper temperature zones. The problem is that it's a "cumulative" effect, so while you say your temperature zones have been incorrect but they've been "fine until now", actually they haven't been fine at all, as what's happened is he's been in improper temperature zones and possibly under inadequate UVB/UVA lighting for a month, and now the effects of this improper husbandry have started to effect his health, because without proper temperature zones he cannot properly digest his food (this is why he's been impacted, in addition to not being able to absorb nutrition from his food), and the lace of proper UVB/UVA light, if that's also going on, has finally started to cause the signs/symptoms of a calcium deficiency, because without adequate UVB/UVA light for at least 13-14 hours a day, he cannot absorb, process, or use any of the nutrition/vitamins/minerals from either the food he has been eating or from the supplement powders you've given him. It's very common for this to start happening about a month or so after a person brings home their baby, as it's just been enough time for the improper lights/temps to start to cause issues.
What
UVB light do you have? (Brand, wattage/strength, and type, meaning is it a compact, coil, long tube, or Mercury Vapor Bulb) Is your
UVB light sitting on top of the mesh lid to the tank, or do you have it strapped to the underside of the mesh lid? How far away (in inches) is the
UVB light from the basking spot/platform your dragon sits on to bask?
What type of Basking Bulb do you have? (Meaning wattage and color of the light) How many hours per day do you leave both your
UVB light and your basking light on?
I guess you don't have a proper thermometer, meaning either a Temperature Gun or a Digital Probe Thermometer, probably only using a stick-on thermometer of some kind? You already know that you have no way at all of measuring his Basking Spot Surface Temperature if you only have a stick-on thermometer, as they only measure Ambient (air) Temperatures, and this is very important, as without a Basking Spot Surface Temperature within 105-110 degrees F your dragon cannot properly digest his food, and if the Basking Spot Surface Temperature or Hot Side Ambient (air) Temperature is over 110 degrees F, then this is getting into the ranges that cause dehydration, and if over 115 degrees F they can be lethal for long periods of time. So buying a $10 Digital Probe Thermometer at Petco, Petsmart, etc. is very important ASAP.