Hi there. I have successfully raised a cottontail before (see my avatar). Most resources will advise that cottontails should not be kept as pets and they should be returned to the wild or brought to a wildlife rehab specialist. A cotton tail at 6 weeks old will do just fine on his/her own in the wild at this age. If you do elect to release him/her, you should only do it at dawn or in the early evening in areas where you have seen other cottontails.
If you do decide to keep this bunny as a pet, you should note that this is a different species than typical European domesticated bunnies. This is an animal that may not end up letting you pet or hold her. She's a wild bunny and she may not ever be a cuddly pet. It's just something to be aware of as you take on the responsibility of being a new pet owner.
In terms of feeding her, at six weeks she should be completely weaned. Fresh grass without pesticide is really important, as well as timothy hay (which you can buy at the pet store), compressed alfalfa or timothy pellets (buy the juvenile diet), fresh greens, such as kale, and lots of water. If you are changing her diet, you should do it slowly to avoid tummy upset and diarrhea. Fruits are high in sugar and should only be given as a minimal, occassional treat. Carrot tops are fine, but not the carrots themselves. No corn, beans, root veggies, onions, garlic or leeks.
You should give her the option of an indoor cage with a solid bottom - not wire. You should use soft bedding, not wood chips or saw dust. You should provide her with a litter pan and she should not have much trouble litter training herself. Once she has gotten used to her new home, you should let her out for exercise and play. Eventually you can let her go in and out of her cage when she wants and roam the house. Be prepared for bathroom accidents. Also be prepared for chewing on electrical cords or furniture legs. You can buy cord protectors and bitter apple spray for your furniture legs.
For vet care, you need to make sure your vet is qualified to care for rabbits. You may need to find an exotic vet. I did spay my cottontail.
I hope you enjoy your new bunny.