I would think again about having a cat and a baby. They can do very well together. If you are dead set on not keeping your cat, please try your hardest to find it a home. It is not inhumane to let it outside, but it is much kinder and safer for the cat if you find it a loving home. Your veterinarian and local shelters or humane rescue groups in your area should be able to help you find your cat a new home where her safely can be assured. I hope you reconsider letting her go at all, but if not, please find a home rather than letting her loose outside.