I apologize if this has been covered before. Here's the situation that popped up the other day and both my opponent and myself were unsure how this played out.
Quick Draw is on 3s and 3h. QD gets hit with a Proton torpedo from a Contracted Scout, 3h and 1c; and I blank out on my defense. I lose 3s and then draw a "Blinded Pilot" critical. Yep, sucks to be me. We played it out as I flip "Blinded Pilot" over for the shot after having lost a shield. After the game, my opponent was curious how that interaction would have happened. He brought up the possibility of QD getting his return shot AFTER i removed my first shield token (and didn't have blinded pilot yet) and then received the Blinded Pilot after that, making me give up my shot on the following round.
I was pretty critical in our specific turn, because I was running FCS and Targeting Syncronizer on QD. I was running Pure Sabacc too who (before QD took the Blinded Pilot then flipped it over) had a Rng 1 shot on Fenn Rau (out of arc; Yay!) and rolled 1h spent QD's target lock and rerolled into 4h and 1c. Fenn survived on 1h.
So IF Blinded Pilot was still on QD for the next round, it would have drastically changed what occured the following round. I'll spare you the details, but it basically meant the loss of Fenn Rau and that scout.

So which way was correct? Would Blinded Pilot be flipped on the reactionary shot or on the following round?

When QuickDraw was first released it seemed plausible that her bonus attack might interrupt the rest of the attack sequence, but since then the FAQ has clarified* that QuickDraw's ability happens at the same time as any other "after attacking/defending" ability that generates a new attack. You played it right.

*: FAQ 4.3.2 p13 "If 'Quickdraw' loses a shield token during an attack, the ability triggers during step 9 of the 'Timing Chart for Performing an Attack' on page 8."

@digitalbusker wish I could give extra likes for including the citation

Now for more fun, what happens when Deathrain drops a bomb on her and wants to barrel roll out of her arc before she fires back for losing a shield. No handy-dandy timing chart, and no official answer yet either.

Same timing so init order.

Looks to me like QuickDraw counters when the bomb gets dropped and Deathrain doesn't roll away until after the bomb drops

Deathrain: after dropping a bomb...

QuickDraw: when you lose a shield...

Proximity Mine card text: when a ship's base...

Bomb token reference card#6 (the one with proxy mine) FAQ 4.3.2 pg.2: when this bomb token detonates...

FAQ 4.3.2 errata note regarding proximity mine on pg4: a Proximity Mine token that is dropped on a ship is placed under the ship’s base and does immediately detonate