Yes they can hurt themselves. I'm assuming you have a baby beardie since they tend to be a little more jumpy than older dragons?
It's best to keep anything that is too tall out of his enclosure. It's also a good idea, unless your 100% confident you can keep him from jumping, not to sit him on high places when out of his enclosure. Right now you can try letting him run and play on the floor in a small room like a bathroom. You want to make sure everything that he could possibly get into is blocked off and of course you'll need to sit in the room with him while he plays just to keep an eye out. But this is a safe way for a little dragon who likes to jump to get exercise and play time. He should calm down more and be less jumpy as he gets a little older.