Havana Brown kittens & cats in Prospect, Kentucky

I happened to come across this abandoned young one in a grocery store parking lot. I took her to the nearest shelter to check for a microchip (none found) and since then I have been taking care of her at my place because the no-kill shelters were full. She has had a basic checkup at the vet and appears to be in good health. She was checked for fleas and given a de-wormer but she is not fixed and has not had her shots yet. She is probably more than six months old but less than a year. She’s very friendly, constantly purrs, and is overall just a super chill cat. She’s been very sweet and curious with visitors/friends that have been over. She was even really friendly and compliant with the vet and assistants when she got her checkup. I would like to find her a permanent home ideally with more space than my one-bedroom apartment and hopefully also with a bigger family.