The umbilical cord has exactly nothing to do with anything... if baby is properly dressed for the weather and you are ready for some exercise then taking a walk sounds like a great idea.
Consider a wrap or sling baby carrier for at least the newborn and infant stages, I feel much more comfortable wearing my baby instead of pushing a stroller - less chance of random strangers walking up and touching baby with their dirty hands plus baby is more likely to enjoy the ride being held close and warm and safe. Not to mention you get a little bit of weight bearing along with your exercise :-) never a bad thing!!
I would wait at least a week or two before taking her anywhere :)
I waited until my daughter was about 1 week old.
It's best to wait until the cord falls off in its own
Whenever your comfortable.