The Quickdraw Ability is handled as follows in RAtC:
Possessing the Quickdraw Ability puts the challenger up two traits for the purposes of initiative. In some cases, this may serve as a tie-breaker for other "I go first" situations like multiple characters tied with the Gift: Spirit of the Fray.
Quickdraw also allows the challenger to draw/switch weapons as a free action during combat. Normally, without the use of Quickdraw, drawing/switching weapons after combat begins would be a static Physical test against 7 Traits. drawing/switching weapons is always a free action outside of combat rounds.
By taking a specialization in Quickdraw, for example, "Quickdraw x3 (Pistols)", the challenger will be considered one additional Trait up, as normal, for the purposes of initiative when the weapon of specialization is being used.