Hi and welcome to RDN.
I have a few years experience in doing therapy work with my rotties and other breeds. Some rotties can make wonderful therapy dogs, but they must have a temperment that is the best of the best. It is recommended that for a rescue, you should own and work with the dog for a minimum of six months before considering therapy work. This is because there is a "honeymoon period" when you first adopt an adult dog and any temperment issues the dog has may not become immediately apparent.
You should use this time to get your dog into obedience classes - solid basic obedience commands are required for a therapy dog. Also spend the time socializing the dog with different people - that way you may find out if she is at all fearful.
Also, please have your dog's hip issues evaluated by a vet. It is not recommended for dogs with certain health issues to work as therapy dogs. Chronic pain can cause behavioral issues, also a dog may snap if touched in a painful area.
Before becoming a therapy dog, your dog will be evaluated and tested by a therapy dog organization. The evaluation and testing are difficult, but a well trained and socialized rottie can pass without problems. The two largest national organizations are Delta Society (Pet Partners program) and Therapy Dogs International. Here are the links for the websites:
Delta Society - Improving Human Health through Service and Therapy Animals Therapy Dogs International, Inc.
I prefer to refer interested people to Delta Society as they have a home-study training program which helps prepare the handler as well as the dog. Good luck, I hope you will continue with this.