I noticed today that my bearded dragon has a dull-looking patch on her back. Does anyone know what might have caused this? Is she sick? I'm very concerned. Any info would be greatly appreciated.
Based on you picture, I'm happy to say that your bearded dragon is shedding. All you'll need to do, is make sure that she is able to get rid of it okay.
Reptiles shed their skin as they grow larger, if you got your bearded dragon when she was older, you might not have noticed it before as the older they get, the slower they grow, which means shedding less often.
The easiest way to help, is to give her a lukewarm bath. Fill a container with enough water to reach her shoulders, and let her soak for a couple minutes to help the skin detach. Then you can gently massage her with your fingers, or a soft bristled toothbrush, to help coax some of the dead skin to fall off. It's important that your never pull on shedding skin, if you pull on the skin before it's detached, it can be very damaging to your bearded dragon as that skin is still attached and a living part of them.
What you want to keep an eye on when she's shedding, is if any of the old skin gets left on. Skin that doesn't get shed can build up and cut off blood circulation underneath it. It's a common ailment in bearded dragon's tails, where a couple layers of old skin build up, acting like a tourniquet, eventually leaving that part of the tail to be amputated. Bearded dragon's fingers are also an area to keep a close eye on for the same reason.
What I was worried about when you first said that it was a dull spot, was if the spot was a fungal infection. In that case, you would want to give her a bath with Betadine solution diluted in the water, until it looks like weak tea. You would give her these baths each day, until a day or two after don't see the infection anymore.
Depending on what substrate you have, you would want to either get rid of it, or wash it thoroughly. It's almost easier to use paper towels while the infection is still occurring, that way you can replace them each day. Sand is very good at harboring fungus, so definitely throw that away.
Fungus infections are something where you'll want to find a vet that can handle reptiles for, because while the baths will get rid of the fungus growth, it sometimes comes with infections in their system that require oral medicine.