You can start working on her house breaking and crate training. At this age, she's a blank slate and she sounds very willing to learn and to please, which is wonderful for you!
There are several threads on here about both topics, if you use the search function, you should be able to find them. Crate training is a wonderful tool to keep her out of trouble when you can't be right with her (i.e. you need a shower, go to the bathroom, cook a meal, etc).
It's not unusual for unscrupulous "breeders" to send puppies home anywhere from 4-6wks of age, which as you already said is WAY too young. Many people working at shelters have little true dog knowledge, so when someone walks in and says this is an X old puppy, they just put that down and accept it.
You may want to search around for puppy kindergarten classes also, as she should be old enough to start those ASAP. They'll be great for socializing her and teaching you about training a dog, and starting to build that wonderful bond between you.
Yogi, thanks! He's still a pup, only 10mos, but his body often belies that fact.
