Cows milk is not good for puppies, and she can be totally weaned at this point. If you must give milk, give goats milk, and you should get it from a farmer, rather than in the store.
Eggs are good You can put a little salt in them and nuke them in a a little bowl if you do not want to feed them raw (messy). Then you aren't adding any oil. You can also hard-boil them, and give her one twice a day, broken up over her kibble.
She is not moody. She is a baby who is not ready to be on her own. Lots of pups have trouble eating without the competition of the litter. Some get depressed on their own. If you have another dog, it does make it easier, but don't get a dog for your pup. You have to be mom and littermates for her. This means, playing with her, keeping her safe, providing safe things to chew on, keeping her clean, and giving her lots of company. You might want sleep in the same room with her, have little x-pens in rooms where you spend the majority of your time and have toys in there for her. This way you can be with her, without being 100 percent attention all the time.
She should be sleeping a lot. No walks -- she is just not protected by vaccines or anything, and she is too small to do forced marches. Just keep her in your home, and work on potty training in the back yard. Let her determine exercise. Be very easy on steps at this point.
Heidi Ho, Odie
Joy-Joy, Bear Cub, Hepsi-Pepsi
Cujo2, Karma Chameleon
Ramona the Pest, Kojak -- who loves you baby?
Tiny Tinnie, Susie's Uzzi, Kaiah -- The Baby Monster.