Hi and welcome to YT. I think it is fabulous that your able to rescue this puppy. I'd be sure to have the puppy seen by a vet ASAP. Since the pup is from a rescue, and very young, she needs to be treated for parasites, and kept indoors all the time. She is too young for vaccinations. And the concern is Parvo, Distemper, flu, because she has been around other dogs , she is at a high risk.
As far as I understand, rescue groups do not just adopt out to just anyone.