I would have to euthanize a kitten with leukemia?

I found a kitten in a container and he took to a veterinarian. He tested positive for feline leukemia with with upper respiratory tract infection and I have four domestic cats at home. Kittens are assumed to be older than four months.
I think I should take-home and expose my cats to the virus, but no one else would take, so I made it my local animal shelter, and they said they were going to euthanize it. As a cat lover, I feel horrible and I read a web article that you shouldn't euthanize a kitten that tests positive - you must give this time.
I'm not doing what I did? Should I take the kitten before it is too late? I believe that I made the good overall, but I wonder if I should have given some time, although I do me forgive never if my other cats were transmitted the disease or the URI.
In addition, I would have had my other cats vaccinated for leukemia (which I intend to do so in all cases), but my vet told me that there was still a 20% chance that they may become infected at a given time.