It is about the same rules as hamsters. Proper cage / brooder, bedding, heat, food water
Wash hands after holding and don't let her on counter while preparing food.
I have rescues in my house that are adults. They are in separate cages in the storage room.
Contrary to popular belief. Chickens are not nasty creatures full of disease. You will enjoy having your chick inside.
Also my bigger hens have made the stray cats fear chickens. I can not speak to your population. I do recommend looking into a trap and release program. I did that here I trapped cats took them to humane society, they spayed / neutered and I picked em up and set them free here again. Lessened the kitten problem by thousands!
Congrats on your new home
Good luck