Yes, a good and interesting piece for sure. Certainly, I'm looking forward to reading more.

You have want to know, if there anything going on that leaves you confused or wanting more explanation? Yes, there are a few odd lines. Now, I realise this more than you're looking, but I can't help myself, so I've also given a few other examples. Please bear in mind that much of this is just my opinion. Others may read your piece quite differently.

Her small body huddled beneath the ragged, torn blanket, Elizabeth cried.
This opening line confused me. To me, it reads too much like dialog. Maybe the second commas could be a period?

The sobs echoed in the hall; despite its size she was the only girl here – all the others were at supper.
This reads oddly to me, too, because of the punctuation. I realised what you meant after I had re-read it, but it made me stop and have to think for a moment, and that's exactly what can break a reader's feeling of suspended believe. (Now, that's just a fancy way of saying, it's not a smooth read) Also, people who know a whole lot more about writing than I do, always say, write your story then cull as many words as you can without losing any of the description or story. That is, less words to say the same thing, while not sacrificing any of the description or story impact, will give your work a tighter, smoother feel. "All the other girls were at supper tells me she was alone—you don't need to repeat the information. E.g. All the others were at supper. Her sobs echoed in the hall, despite its size.

Certainly, I'm no expert, but I found some of your punctuation a little odd. I've never actually seen colons used so much in story writing. Again, it could be just me. I found it distracting.

Headmistress Constance had also added forty strokes of the cane this time, twice as many as yesterday, citing continued ill behavior.
Please, don't fall into the trap of telling your readers things that your characters can tell so much better and clearer than you can. E.g. "It would seem that twenty strokes wasn’t enough for you yesterday, Elizabeth", Headmistress Constance told her, "Maybe forty today will cure your ill behaviour?"

.. her stomach growled in dismay..
This jarred me. Stomachs growl, but they don’t do it in dismay.

Elizabeth did not look from under the covers
There's absolutely nothing wrong with this line, but really isn't it just a missed opportunity to paint a poignant picture of this poor little waif?

…and the tears came quickly to her eyes.
Again nothing wrong here, but isn't it a good opportunity for a little description. i.e. Colour of her eyes? Thick heavy lashes?

.. as though the Shadow Thing itself weren’t certain what it could do now.
Again, this isn't a biggy at all, but it was jarring—the Shadow Things is singlar—"weren't" should be "wasn't".

When they stopped next to her bed, they were almost a normal pace.
This sentence reads back to front to me. Shouldn't the sound of footsteps come before they stop?

Now being super nit picky here, use a double hyphen for your punctuation, not a single.

Ok, like I said, it's a great start. You say you haven't yet introduced the plot, but I don't entirely agree. We know exactly who Elizabeth is and her circumstances. Already you have us, your readers, intrigued to know more; wondering what will happen and how, and that's an excellent start to any good story.

Basically, you've fed me just enough plot to make me hungry for more.