Place to rent or room ASAP

My name is Carla and I am a 31 year old female.
I'm quiet, clean, responsible, honest, keep to myself, and a hard worker.
Looking for a place to rent ASAP before the end of May.
Need to move quickly because of a domestic violent situation.
I do not drink, don't smoke, and don't do drugs.
Have one cat that is fully house trained and registered as ESA.
I am hoping for at least one bedroom place or two bedrooms.
I can afford no more than $1,200 a month.
Any help is gratefully appreciated.
I am looking anywhere in Virginia except for Richmond.
I am willing to rent a room, basement, garage apartment, or anything.