Oh, dear! No this is not normal and your beardie sounds like they should be taken to a vet as soon as possible. If there is a bit of flesh coming out of it's vent that means that your beardie has prolapsed (do a site search for prolapse and you'll come up with lots of info). You need to keep the prolapse moist until you get your baby to a vet. Try soaking your beardie in sugar water..... dissolve a couple tablespoons of sugar in warm water and dilute with some room temperature water and soak your beardie in it. Sugar water reduces the swelling. If you have any hemroid cream or water soluable personal lube, both of those will keep the prolapse we until you get your beardie to a vet. VERY SERIOUS CONDITION.... please act now if the prolapse hasn't retracted back inside.
Beardies normally lay eggs in clutches (more than one egg at a time) so if your beardie laid only one egg, that could mean that she is egg bound, also a life threatening problem that needs vet assistance. Are you sure it wasn't a large bit of urate that had hardened due to too much calcium supplements? Sometimes passing large urates that are hard can scratch the inside of the beardie while it goes to the bathroom. This will cause the inside to swell and prolapse.
Your beardie must be very upset..... try to keep her calm until you get the the vet. Warm temps, wrapped in a towel after a soak in sugar water and an application of hemroid cream, and lights out will help your beardie stay calm and not scratch the exposed insides further.
Good luck and keep us posted!
Kailin