How To Take Care Of A 6 Week Old Kitten?

My 6 week old kitten has gotten really sick. She is very lethargic and won’t eat or drink. She also seems to be in pain. I have tried giving her warm water mixed with a little bit of coconut oil but she doesn’t seem to want it. The vet said that if he can catch an infection early enough, they can treat it successfully without having to put her down because of the liver failure, which was what happened when my cat got sick last year at age 2 years. He gave me antibiotics for this sickness and recommended getting another kitten sooner than later so we could get past this one’s illness without losing another pet…can you please tell me how long before i should expect the other one? The elder brother is still around thank goodness!