I'd let her settle in for a bit before handling, some beardies are fine to handle when you get them but if they're not eating and are still settling in and being lethargic then I'd leave them alone for now.
Does the night time bulb produce any light and what temps does it get to without the heat during the night?
If it produces light you have to get rid of it as beardies see in all color and red/purple/green/blue/black lighting can keep them up during the night and mess up their eyes a bit.
And if it doesnt drop below 65 during the night then you need no night time heat at all, if it does however you can use a CHE (ceramic heat emitter), this produces no light and only heat.
Are the temperature gauges you have digital ones with probes or are they stick on ones?
Do you have UVB for her at all? If not then this is why she is not eating and being lethargic, beardies need UVB to survive and be healthy, without it they die a slow painful death as they develop MBD.
https://www.youtube.com/watch?v=qMvShx_hxDI
This video shows a severe case of a bearded dragon with MBD, because it got so bad they had to put it down.
And just so you know all UVB bulbs are not the same, a exo terra compact/coil bulb wont be the same as a zoomed compact/coil bulb, and a exo terra tube light wont be the same as a zoomed/reptisun tube light. Theres good and bad brands for different things, exo terra sucks at tube lights but works "okay" in the compact/coil section, meanwhile zoomed does tube lights pretty well but all of their compact/coil bulbs fail to produce any good UVB.
Anyway make sure you have a tube light going over her, it should be a Reptisun T5 HO 10.0 22" at the very least. Also know that your going to have to upgrade her tank to a 75 gallon soon as 75 gallons is the minimum for an adult bearded dragon. 40's and 50's just dont work for beardies above a year old, beardies are generally 18-24 inches in length and are fairly active and also semi aboral so the space that 40 and 50 gallons offer just dont cut it for them.