Harzel
Adventurer
On your 8a, an invisible creature not attempting to be stealth flying within 20', especially at double normal walking speed, in heavy armor, should be noticed. The way not to be noticed is to use the hide action. I might ask for a perception check to identify the space the flying, invisible creature is in (absent the visible flying wand, natch), but to be aware of a creature moving through the room? Nope, you get that because the invisible flying creature is not attempting to be stealthy, just invisible.
Yes, I phrased it too tentatively. There would have to be some significant extenuating circumstance for her to not notice.