He's darkening to absorb as much heat/light as possible. That's completely normal..
Unfortunately, the 13 watt
UVB light is completely inadequate UVB for a bearded dragon, it's not anywhere near "perfect for a baby", don't believe anything a pet shop clerk tells you, especially if it was a Petco or a PetSmart...In addition, if you have the already too weak
UVB light on top of a mesh lid, the lid is blocking up to 50% of the already too weak
UVB light. That particular bulb, to be effective for a bearded dragon, would have to be mounted inside the enclosure and be unobstructed by anything, which is fine, most actually cannot sit on top of a mesh lid, but a 13 watt
UVB bulb would have to be within 2-3" of his basking spot to be effective at all, which is not safe for his eyes, and is almost impossible to achieve anyway. If you bought a "Bearded Dragon Kit" most everything in it is going to have to be replaced, the basking bulb is fine as long as it's bright white and not a colored bulb like red, blue, yellow, green, purple, etc., and as long as it gets his 3 major temperature zones/gradient within the correct ranges, but the
UVB bulb is not adequate, and if it came with any stick-on thermometers they are not adequate and are usually off by up to 20 degrees or more. If it came with a digital thermometer with a probe on a wire then that's good, that's what you need to #1) take accurate temperatures, and #2) take the temperature on his basking spot, which you cannot do with a stick-on thermometer, you can only take ambient air temps, and as I said they are usually off by around 20 degrees if you test them. So if that's the case your temps are most likely too low, though your enclosure is very, very small, so you won't need a high wattage basking bulb.
You're going to have to get him a much larger enclosure soon, it's impossible to establish a proper temperature gradient for a bearded dragon in that small a tank. Beardies come from the Australian desert, and because of this they have very specific and unique lighting and temperature requirements in order to grow properly, process calcium and build their bone density correctly, absorb nutrition, and basically live and survive. They need a Basking Spot temperature between 105-110 degrees while babies and juveniles, and for adults they usually like it a bit cooler, between 100-103. This is where they go after eating to digest their food, so this is very important (and the reason you must have a digital probe thermometer and not a stick-on). The Hot Side of the enclosure is the side that contains the basking spot, and the ambient temperature of the Hot Side needs to be between 88-93 degrees, so lower than the basking spot temp, which will be very difficult with that size of tank...but even more critical and more difficult to achieve in that size of tank is going to be the opposite side, or the Cool Side, which needs to be considerably lower, between 75-80 degrees maximum, so he always has a place considerably cooler to go to at any time he want to in order to cool down. (FYI, the maximum temperature anywhere in his tank should be 110, and his cool side should not ever go much above 80 degrees) So a 20 gallon long tank is the general minimum size for a baby or juvenile because it's the minimum size that you can establish a proper temperature gradient.
As far as the
UVB light, as I said, a 13 watt compact
UVB light is not even close to adequate for a bearded dragon, and this is the most important piece of equipment you'll need to buy for him and to replace on a regular basis in order for him to stay healthy, keep having any appetite, to grow, and to live. There are very few adequate UVB bulbs made for bearded dragons, even the ones that are labeled for bearded dragons, unfortunately. What you want to buy is a long UVB tube, either 18" or 24" long (your current tank will obviously need an 18" long one, but eventually you'll need to upgrade to a longer one, but for now an 18" tube is fine). Never buy ANY bulb that is a "coil" bulb, they all seem to cause serious eye and skin issues. Most compact UVB bulbs, like the Exo Terra one you have, or the Reptisun 10.0 compact
UVB bulb, which is also only 13 watts, are not adequate. Mercury Vapor Bulbs (MVB) emit both UVB, UVA, and also the heat, so they're all in one bulbs and are very good in general, but you cannot use one with that size of enclosure. So you need to buy either an 18" 10.0 Reptisun T8 UVB tube and a matching length tube fixture, or an Arcadia 12% UVB tube and the same matching length fixture (the higher strength Reptisun 10.0 T5HO UVB tube is usually recommended, but they're having a recall right now, so I'd not buy one until they get the bad ones off the market, so stick to the 10.0 T8 18" tube). Both of these tubes will absolutely have to be mounted INSIDE the tank and under the mesh lid, because they are not strong enough to penetrate the mesh and still provide adequate UVB to your beardie. They also both need to be unobstructed by the mesh lid or anything else (some long tube fixtures have a clear, plastic safety cover over the tubes that must be removed as they block all the
UVB light emitted), and within 6-8" max away from his main basking spot, so whatever decor you're using as a basking spot/platform will have to put him within 6-8" of the unobstructed UVB tube. Both of his lights, the bright white basking bulb and the UVB tube must be on for at least 14 hours every single day. No heat source needed at night as long as his tank stays at least at 65 degrees, which most houses do. They like it pitch black and cool at night, just like the desert.
Also, if your kit or the pet shop employee recommended a loose substrate for the bottom of the tank, like a calcium or "repti" sand, crushed walnut shells, bark, wood chips, coco husk, gravel, or any other loose substrate, please dump it out immediately and put down clean, dry paper towels for the time being, and replace them as they get dirty. Loose substrates are simply impaction risks to bearded dragons, especially young babies and juveniles, and also harbor bacteria and fungi. They cause nothing but health issues and literally often cause death, and are not natural for a bearded dragon, as the Australian desert is solid, rocky terrain, not sand. You can use textured tiles, non-adhesive shelf liner, carpet, fleece, newspapers, or paper towels as your permanent substrate, but in the meantime if you have a loose substrate, get it out of there and just put down paper towels.
For the meantime I would find a way to get that 13 watt Exo Terra UVB compact bulb UNDER the mesh lid, either by cutting a hole in the mesh directly under the bulb, or by removing the mesh lid all together, and then find a way to raise his basking spot platform closer to the
UVB bulb, at least within 6" of the unobstructed bulb, until you can order or go buy an 18" 10.0 (never buy a 5.0 or lower!) UVB tube and fixture for him and get it mounted properly inside the tank and within the correct distance of his basking spot.
