Another huge wall of text because of msg cap

Owl girl sounds interesting owo
Your numbers a bit wonky, but that's super easily fixed, and I'm not gonna worry too much about that and just lightly glaze over it.

Q sounds super fun to use. I have very little qualms with this, outside of the numbers; 150 to 300 is too high. I'd settle for something around 80 to 200, since this seems to be your main damage ability, and it's also an AoE. I'm also not sure there should be a second effect based on whether or not you dash to an ally or an enemy at the end. It just doesn't seem to necessary.

Your passive has too many passives-- especially since your W has its OWN passive. Even two parts to a passive is a stretch, and two passive parts are really only necessary when the main part of your passive has no direct impact you can feel as raw power (see: Ornn). If I were you, I'd scrap Feather's Strike, for reasons later mentioned. Doing so lets you pump power into the more active part of the kit, which always feel more engaging. Hitting Gnar's R always felt better than proccing his mini form W :P

I'm not sure where the magical crits come into play; while it's COOL, and may fit thematically, it doesn't make much sense to me for gameplay, and there aren't very many itemization choices. For example, the only AP and Attack Speed items are Nashor's Tooth and Guinsoo's Rageblade; you're kinda forcing them to build both of those, which might not feel too good, and you shouldn't rely on very specific items to be effective. If there were more itemization choices for such Champions, it could definitely be a thing, but there just really isn't. I'd say to just go for your autos dealing bonus magic damage on-hit, and MAYBE, if you're still feeling the AP autos, give them attack speed scaling with AP instead of crit.

The W cooldown mechanic is interesting, but you have the flaw of not being able to use it outside of when you get kills or 5 seconds after you kill a camp, which can kinda feel bad, since in Champion-to-Champion combat, you're down that ability early game until after you finish a gank. If you can get around this somehow, this is a really cool ability. There should also probably be an AP-scaling on the heal, though.

Your E is also interesting, and in my opinion, it combos into your kit pretty well if you can use your W with it; I'd suggest a self-slow, though, since that can possibly be pretty easy to get off. I'm also not sure how I feel about your EQ interaction; the idea of the interaction makes a bit of sense, but an AoE stun like that is really strong, and I'd look at something outside of "AoE stun + damage." If you really wanted to keep the effect your Q has when you land on a target, I'd consider moving the stun onto that and the initial collision. Just a random suggestion, and that potentially still has issues I didn't consider, so if you find something better, go ahead.
Numbers-wise, the scaling is WAY too much, and your base damage is way too low; this is potentially a 300+% AP scaling, which is pretty huge. I'm not sure how I feel about the range increase.

R is... really strong. You can potentially go full tank, flash into the enemy team, R, and have everybody land on a Veigar W at the end of it. There's counterplay for things such as Amumu R, which is probably something we can relate this to, but the way this functions lacks too much of it; since you're pulling people to the center, it's an INCREDIBLY easy setup, and the basic existence of the idea of being a tanky ult bot might sway people away from building as an AP assassin-esque caster, which is probably what you were intending, considering they don't have too much CC. I'm also not sure how this fits into their gameplay thematically.
This reminds me of a DOTA 2 hero named "Kunkka," who has this on a basic ability, but it's a single-target spell and returns them to their original location, rather than allowing them to have such a big say in where they land.

Overall, outside of the ult, you've got something really solid here. If I were you, my next steps would be to look for refining the passive, messing with EQ interaction a bit, and looking for a new ultimate for her.