Please, PLEASE take it to a wildlife rehabilitator. I myself am a wildlife rehabilitator. I can't tell you how many times I get people bringing cottontails into my shelter that they tried to care for by themselves and failed horribly. Cottontail babies are one of the hardest wildlife creatures to care for properly; even for someone with years of training. I urge you to get it to a wildlife shelter ASAP!
People who are not trained really shouldn't even attempt to feed baby cottontails on their own.
There are probably plenty of these laws where you live that say that trying to raise a cottontail without a license is illegal, if you need more of a "push" to get it to a proper rehabilitator.
If you are helping this bunny because you feel sorry for it, I prefer you not leave it off at wildlife centers that take in birds of prey and small carnivores primarily for reasons I think you can figure out on your own. Find a rehabilitator that cares for only wild rabbits and squirrels. (IF possible. If not possible, go with the next best option.) Avoid facilities that have multiple volunteers caring for individual cottontails - that never works out well. In my shelter, only ONE person is allowed to even feed the cottontails. We keep them in a little area far, far away from anyone. And the person in-charge of those particular babies only feeds them when needed then doesn't touch them. No human interaction. No matter how "cute" they look, you ONLY touch them when they need to be fed! There needs to be a harmonious balance between human contact: and remaining wild like they need to.
That's why only a professional should be allowed to raise them.
Early mortality due to lack of Colostrum and natural milk factors is a huge killer in baby cottontails.
This is particularly a problem in babies that are under 2/3 weeks of age.
Cottontail mother’s milk has protective ingredients called,"antimicrobial fatty acids", that artificial milk replacements cannot duplicate, like kitten milk replacement. Their first milk (colostrum) is very rich in an active form of vitamin A called "retinol" - something not found in replacement formulas but essential for normal development.
I know you are probably trying to take care of this baby out of the kindness of your heart, but please, take it to a wildlife shelter.