This young woman is ridiculous. IF she really does have anxiety problems, it's no wonder. She doesn't know how to get along with people.
All the other roommates need to go to Home Depot or Lowes and just buy sets of these exterior door knob locks for each of their bedrooms. Buy them all at once, and simply hand her the receipt. Have the building superintendent install them. Also hand her the bill for how much it cost to have him install them along with the lock. No discussion, just collectively put on the locks. They all should be able to have a reasonable expectation of safety and privacy. If she can't understand that, she has more problems than a dog will solve.
It shouldn't be much work to install the locks. These types of door knobs are universal. He just has to take off the old ones and slide in the new. The holes for it should be the same. The salesperson at Home Depot can help the girls get the right ones with a keyed lock on one side and a knob to turn on the inside. It needs to be the kind where someone can't slip in a credit card or hotel key in the door jamb and be able to push the door open. So no simple "bathroom door" or interior lock. They don't have to be expensive since the locks aren't going to outside doors. But, they want to have a reasonable lock to keep people out and their belonging safe inside an apartment. A decent one will run about $20. A pick-proof one will be more, like about $40. Considering there will be people who may just be sitting around for hours, they may try picking a lock, since there will be no witnesses around. Something to think about.