She cast a specialized version of reparo on Harry's glasses before she ever even attended a class. Also she said she practiced all her spells at home before ever getting on the train which throws a lot of crap into question...
That's... great? Yes, she's quite intelligent and talented at magic, but we're talking about inventing spells, which is a high-end skill and quite different from adding modifiers to spells.
...With this approach, we'll quickly turn Dumbledore into an enemy, or at least make him highly suspicious and thus potentially restrictive.
Think of how this will look to him if he ever catches wind of it: a bright student with skill far beyond his years who keeps his secrets close to heart forms an inner circle (OOC, we've even been discussing the relative usefulness of friendship choices) and has those in it learn occlumency so that they will be better at keeping his secrets. With it being obvious that we'll end up training everyone in that circle in magical and non-magical combat, what message does that send and whom does that behavior resemble?
That we've been trained in CONSTANT VIGILANCE and don't want the secret to our power divulged in an uncontrolled manner. We've made the decision to hide this from Dumbledore for now, and will hopefully be able to determine whether we can trust him with it in the near future. For now, we need to actually
stick with our decision. Because by just telling them right now we might as well tell every unscrupulous Legilimens in the castle (I'm looking at you, Voldemort).
Besides, we have no viable way to teach them occlumency aside from Gamer mechanics, and that defeats the whole purpose.
Party mechanics aren't a certain way to teach them either. It speeds things up for them, but we don't know by how much. What if it still takes weeks/moths, even with increased stats?
Now, moving on from that, even just knowing that there is a secret may be enough of a tell for Quirrelmort to not risk letting Harry become a greater threat - it's one thing to know that your opponent has been trained by Alastor Moody and is competent beyond his age; it's entirely another to know that there is a secret beyond that which you are not privy to. This makes telling or even hinting about it to anyone without mental defenses not a bit suicidal. From this perspective, if we were going to tell them, we should have done so during the summer, when we had had the time and opportunity to take precautions.
We're his prophecised nemesis, and he's going to try and kill us anyway. Heck, he tried to kill Harry
in canon, and that guy was as clueless as it gets.
P.S. On Occlumency: the idea of using our low-rank Legilimency on our 11 year old friends' immature minds sends shivers through my spine. What the hell, people? They are kids, and they don't have the same perks as Harry to let them shrug off the trauma of repeated mind rape.
So better to leave them unprotected when Voldemort takes a peek?
He's not going to be nearly as careful as Harry.
So raise Wisdom, unless she wants to invent Mind Blank from the base HP magic theory, or devise a tinfoil hat enchantment.
The problem is as always
time. Yes, she can raise her (probably low) Wisdom, but how long until her talent for Occlumency is high enough?
And why do we need Hermione to invent any of those spells? Our potential rate of advancement (including skills) is much higher, and them learning Occlumency can be a stop-gap explanation until we devise a better solution like the tin-foil hat or a Mind Blank equivalent.