Since you don't know how long she has been out there on her own, she might have been without food for several days at least. As you know, that can impact the liver and cause her to lose her appetite. In your place, I would force feed her A/D - you must have experience doing this if you can draw blood. You may want to give one run of sub-q fluids also. Once her body has balanced out, she should be fine.

I had two cats with feline leukemia, they were born with it. Roo was the runt of the litter and his digestive system was not fully developed; he lived only 8 months. Seshat lived for 7 mostly healthy, very happy and rambunctious years. She did get tired a little more quickly than her FeLV- brother and she did take a few days longer to recover from the couple of viruses they got over the years (he got them first and passed them to her). She died over five years ago and I'm sure there have been advances in caring for cats with this disorder, so you could have 10 years with her.

I'm very glad you are looking into keeping her, she sounds like a wonderful cat and a great companion for your dog. I'm no help with names since I'm having a hard time coming up with new ones for my own.