A phoenix would definitely qualify as a special pet, and one that would be welcomed.
Sorry for missing the question, Meliai. Yes, I will be handing out xp and allowing you to improve your characters. Note that I will not allow you to spend it as soon as you receive it, but there will be periods that I will allow spending.
I am very open to adding both Qualities and Drawbacks to the list. I just added a Drawback today for Muse (Big and Slow), and am still working on the Improved Animagus Quality.
I'm not a fan of "overconfident" style flaws. They almost never matter, but when they do it's usually death. I'll try to think of a curiosity-related one, maybe a -1 penalty during classes because she's always so tired from staying up late and exploring. Does that sound like something that would interest you for her? Alternatively, there is always Flaw (Any), which just gives you -1D to any ability if you can justify why. I definitely recommend it.
Also, given her agility and her "legacy," would you see her as a member of the Quidditch team for her House?
An owl is fine as a pet, and Muggle Studies is missing from her list of "others," as you have History of Magic twice.