Hatchling bearded dragons (and other day time lizards) are often active at night, my water skink often midnight raided her salad / softened pellets and hunted down crickets quite late at night , and often could be seen watching TV. Similarly with my bluetongues, and adult and now juvenile beardies (Peppa and Toothless).I often hear bangs coming from Peppa or Toothless's tubs (100L rearing tubs) as late a 1am, and when I look , I see him or her chewing away on something they've caught (a cricket) or at their salad dish having a late night snack. There is nothing wrong with this , only light in the room will be that coming from the TV, my laptop on the coffee table and subdued light from a 4ft fluoro in the kitchen (about 20ft away), so it's not brightly lit up once we turn off the dining and lounge room lights.
If it gets cooler than 24oC in the room the little hatchling is housed, definitely provide a warm area in it's tank to sleep , either
-- a thermostat controlled ceramic heat emitter (mushroom shaped globe that ONLY gives of radiant heat , be sure to mount it in good quality all ceramic socket as they get HOT and plastic sockets will soften and melt and may even ignite and fail), the CHE needs to be on timer to come on when the UV and basking lights are turned off
or
-- a thermostat controlled heat pad (under the tank , or better inside the tank but sandwiched between 2 layers of ceramic tiles), this can run 24/7 and all my lizards have them in their tanks and rearing tubs and they ALL LOVE them, for my adult, hatchling and juvenile beardies I set their "HEATSLABS" to 37oC and their hides are on top of their heatslabs.
Crickets : a 4 - 8 week week old hatchling will take 20day old crickets (10-12mm long), good idea to feed/gutload the crickets with dry straight out the bottle repcal adult beardie pellets + carrot (fresh) and buk choi greens (fresh) and to dust the crickets (in a separate jar) with calcium dust daily , and a mix of calcium dust and vitamin dust 3 days a week.
2 - 3 live insect feeds per day for a very young hatchling , allow a couple of hours in am for the hatchling to warm up before first feed, and at least 3 hours after the last feed before lights out.
A 15 - 16 hour day is appropriate for hatchling bearded dragons (this will simulate summer (breeding season) daylight hours in the natural range in central tropical Australia of central bearded dragons and encourage them to bask and take in sufficient UVA and UVB.
Other good insects
-- calcigents / phoenix worms / black soldier fly lavae
-- blowfly maggots and flies
-- silkworms (for your little hatchling silkworms up to 1 inch long are ideal, live silkworm moths are good too)
Your UV source needs to be the most intense reptile UV tube or CFB you can get , rated at a minimum of 30% UVA and 10-12% UVB, I use 26W UVB200s for my beardies, and allow the beardies to get within 6" of their UVB globes. In their natural range the UVI is typically > 14 during the day, VERY EXTREME UV index.
NO SAND in the tank (especially for a hatchling).
NO WATER BOWL in the tank (will increase tank humid too much). Use the water drip on nose method to give them water, or simply ensure they have access to fresh grated carrot and buk choi greens daily - will provide moisture when eaten, and live insects are an excellent source of moisture too, note bearded dragons have evolved to survive in central tropical Australia's deserts, spinefix grasslands / sevannahs and dry woodlands, can go several years with NO STANDING water in these areas and with little or no rain (even during the summer - cyclone / monsoon season).
Kale is excellent, so are buk choi, puk choi, dandelion greens and flowers, nasturtium greens and flowers as staple greens.