Questioning Quinn's Q's Hitbox

I ran into a case where, as Quinn, I waited for a Kat to Shunpo me to Q her, shooting it backwards to hit her. Problem is, she teleports to the target. So as Quinn it is impossible for me to Q her, due to her shunpo to dodge or just because she is on me. Is this right?

And I know I can E then Q after she Shunpo's too, but this is specifically questioning if Quinn's Q cannot hit a target on her by design.