Learning Over Break

So it's Easter break and I'm home. I'm happy to say that Hermione is going to be allowed to go back to college with me on Monday. This is great as I only have classes two days a week and I'll have plenty of time to work with her.
In the two weeks since we got Hermione, while I've been at school, my mother taught her to sit. She does this consistently. Leash walking is still in progress. I walked with her yesterday. I held a treat down at my side, and every time she stayed at my side for several steps, I gave her the treat. One problem with her is that most dogs pull when they are on a leash. Hermione refuses to move. It rather reminds me of the time I tried taking one of my cats outside via a cat harness. We have the same problem trying to get her up and down stars. She really wants nothing to do with stairs and she's only ever managed to go down so far, and even then it's because she was stuck in the upstairs hall way all alone with everyone else downstairs. She's going to have to learn soon though because I don't fancy having to carry her up and down the stairs to get in and out of my dorm room.
We started the "stay" command today. She caught on really quickly. Only an unusually close encounter with the still unexplored cat caused her to break the command. The cat has been a point of fascination for Hermione. Sabrina, the cat, won't let Hermione too close because of some bad experiences with the lab. But in 2 weeks of having this dog around Sabrina has gotten closer to her than she ever did in the several months of having the lab around. She too evidently has realized how gentle this puppy is.
Hermione is also starting to learn how to go to the bathroom on command, however it takes a few minutes after stepping outside to get her to turn off play mode and focus on bathroom issues. She has the helpful habit of always going to the bathroom in the exact same place. That's nice to know because it gives me reason to believe that if she has her own habit, she will be less likely to break that habit and go in an inappropriate place as was my problem with the lab.
Hermione is also doing better in the play department than she was when she first got here. She was always in lying in her crate and the only toy she enjoyed was a cloth squeaky bone. She now has a couple of new favorites which she plays with constantly. The toy in the picture is a cloth fish with a hole in it's stomach and several squeaky eggs inside the stomach. The goal is to get the eggs out. It gives her something to work towards. She caught on immediately squeezing her nose in pulling out eggs. She also uses the eggs like balls. Her other favorite, and the one we use to coax her into going places she's uncertain of, is a quacking duck. The duck is in the second photo. This one appears to be the absolute favorite. It gets her outside at night when she is reluctant to move, and it also gets her toward the steps even if it's not enough to encourage to go up them.
Tonight, befor Hermione gets too tiered, we're going to try and tackle the stairs. My hope is that if I put something she wants on every step, she will be encouraged to move up eating as she goes. Then, if it's still nice and light, we'll try for a walk.