Hi,
As a licensed wildlife rehabber, I can assure you that you made a good decision in taking the cottontail to the wildlife hospital. It is illegal in most states to be in possession of wildlife without proper permits. Cottontails are also the most difficult species to raise in captivity. And I can assure you that if this rabbit were 6 weeks old....you would not be able to handle it unless it was seriously injured or sick. To give you an idea of how a cottontail develops....it is born totally helpless and is a dark purple/black and is many times mistaken for a mole. They have their fur by 5 days. Eyes open 7-10 days. They can technically live on their own by 14 days but are not fully weaned until 21 days. They are lactose intolerant and can't digest high levels of lactose....the professional formulas we use are low or trace lactose. Goat's Milk or Kitten Milk Replacers are totally inappropriate for rabbits (or any other wildlife) as they do not contain the proper nutrients. Few cottontails have a sucking reflex and they are easily aspirated. They also have a very quick and violent weaning....and that weaning is when most cottontails die in rehab. They are also very prone to death from just the nick of a tooth of a cat (as are most small mammals and birds) due to the population of harmful bacteria found in a cat's mouth. And we have done everything perfect and still have some die on us and the volunteers of my rescue have some of the most advanced cottontail protocols in use anywhere.
I know this is more information than you asked for....just hoping to educate others. Wildlife requries specialized care and formulas and if they are sick, injured or orphaned....there best chance of survival is in the hands of properly trained and licensed rehabbers.
Randy