Umm no a Double Weapon works exactly the same as if you had a Longsword/shortsword combo. So if you move you get a single attack only and only during a Full-Round action can you get to Two-Weapon Fighting.
I always thought that the bonuses were "slightly more beneficial" for a double-weapon (ie, that that was the point of using a double-weapon). Guess I was wrong. Bollocks.
NM.