(Not a champ designer or on the balance team, so this is just my opinion as a frequent MF player)
TL;DR: I think this would make her a lot stronger than it might seem at first.
First, just some general thoughts on her passive:
Movement speed is really, really powerful. Especially +70, which puts her at 395 without boots (that's faster than a Master Yi with Boots of Speed). This speed, combined with Q, allows her to bully lanes pretty hard early, so it's important to have it get knocked off in lane. That gives windows to fight her "fairly".
To the suggestion of preventing minion aggro from dropping it:
It's usually the caster minions that knock off the passive, since you're shooting Q through them to harass. And that's actually pretty important for gating her harass ability. If they didn't do this, you could harass with impunity, and then rush at them with ~400 MS with no downtime.
She would essentially have all of her current harass power, PLUS the ability to rush at you like Draven does. Only she'd rush at you with her auto->Q pattern*, and the ramping magic damage (and grievous wounds!) from Impure Shots.
As small of a change as that might seem to be, I really think that would put her over the top. If we made that, I'm afraid we'd have to trim some of her more obvious power. And at that point, I'm not even sure it's an overall improvement.
*To compare to Draven some more:
At level 3 (two points in Q), Draven's axe does (total AD + 55% total AD) damage, while Miss Fortune's auto->Q combo does (total AD + 85% total AD + 35) to the main target. That's a bit more damage up front, and probably evens out at around 2 or 3 autos. That's about what you'd expect to get from an early level all-in rush like this. Depends a bit on if Draven catches his axes (or has 2 before going in), but it's a similar level of all-in damage.