Posted! :D I'll preemptively defend Dani's spell casting given the extraordinary circumstances they're in as well as the unique method by which Dani casts spells.
1. The adrenaline of being caught in a fight where one could die would make it easier to cast any spell due to heightened emotions and what not.
2. Dani's wand is made of pine, which actually has the characteristic of making non-verbal magic easier to perform.
3. Dani's understanding of incantations as being focusing agents allows her to cast some spells without 'knowing' them, much like the emotional acts of magic performed by children before they're trained. Most other students at her age wouldn't be able to do the same due to the false conclusion that magic is performed by the incantation.
4. The spell is nothing special. It just creates a shield that can take a few hits. As hinted at in my post, it's of a rather poor quality, meaning that two or three more hits would shatter the whole thing, especially if they hit the thin spots, as Dani wasn't able to make it uniform.
5. This is not something that Dani will be able to do out of the blue in the future. In other words, this does not mean that Dani will just be able to cast this spell, or others (i.e. she'll still struggle with Lumos), whenever now. The only reason that she's able to do it now is because a) she has enough time to think about what she wants to do, and b) the adrenaline rush she's experiencing.
If it's still too much, then I'll figure something else out. I just thought that it would be a good way to highlight how Dani works differently than most of the other students.
Also, sorry if I came across as pushy or something with the above. I just didn't want you guys thinking that I was trying to make my character out to be the most powerful or whatever. That's not the intention, and I fully plan on exploiting Dani's many weaknesses in the future. :D