Ok, first of all, if you haven't named her already, you should name her Faith!!

I am thinking a month may be too long to wait for medical attention. If you could find a rescue group, they could cover the medical bills, socialize the kitten, and get her in a good home. I know it would break your heart but sometimes it is the best thing to do.

Has King ever been with cats before? If you decide to keep the kitten, you might want someone else there with you when you do the introduction because the situation could get bad if King doesn't like cats I have a TON of dog/cat intro information so let me know if you decide to keep the cat.

Oh, by the way, I have no clue how much it would cost because prices tend to vary a lot in different areas.