Simple RAW for 3.5: 38 pages, and I still don't know how to play D&D

[St Fan]

Q 6

If you trip an opponent in melee combat, you immediately get a melee attack against that opponent as if you hadn’t used your attack for the trip attempt.

For a character with Improved Trip, can he first succeed in a trip attack barehanded, and then draw a weapon (as a free action with Quick Draw) to make the follow-up attack? (Eventually with Iaijustu Focus...)