Would you let the Iaijutsu ability of the Magus (Kensai) (gained at 7th level) count as "Quick Draw" for a feat that required it?
Iaijutsu (Ex)
At 7th level, a kensai applies his Intelligence modifier as well as his Dexterity modifier on initiative rolls (minimum 0). A kensai may make attacks of opportunity when flat-footed, and may draw his favored weapon as a free action as part of taking an attack of opportunity.
Can draw his weapon as a free action, like Quick Draw, but only for attacks of opportunity.
The feat in question is Dueling Mastery
Dueling Mastery
Prerequisites: Weapon Proficiency (dueling sword), Quick Draw, Weapon Finesse, Weapon Focus (dueling sword).Benefit: You gain a +2 bonus on Initiative checks as long as you start combat with a dueling sword in your hand. As long as you wield only a single dueling sword in one hand, you gain a +2 shield bonus to your AC—if you wield the sword in two hands, this bonus drops to a +1 shield bonus to AC.
Although the dueling sword inflicts slashing damage, you treat it as if it were also a piercing weapon when determining the effects of weapons used by a duelist.
Which requires you to have the weapon in your hand already before combat, so neither Quick Draw or Iaijutsu is going to be used, but it is there in the prerequisites...
Probably not - if the feat was less good then I'd allow it, but +2 AC AND +2 Initiative is already a great feat, even without the part that lets it count as a piercing weapon.
If you used a Dueling Sword as a Magus, I'd try to point out much better an 18-20/x2 weapon would be. If you still pushed for the Dueling Sword, I'd probably let you do it because I'd feel bad.
However, no, by the rules, it does not work.
I'd only allow it if it was in every way identical to Quick Draw except the name. This is not one of those cases. I know there's a few examples, but I can't think of any right now. Abilities that replicate Feats almost word for word instead of just granting a bonus Feat.