What would be the best build to get a Little girl swinging pillow as deadly as a fighter swinging a sword build look like?
Well, you will probably be dealing with an improvised weapon build, which has gotten remarkably viable in the last few months.
1) A Ki Focus would be an obvious choice for letting you treat it as magical. You would need to be a monk or assassin to use this, or multiclassed into one of them.
2) The Belt of the Brawler (a level 3 magic item) lets you make improvised weapon attacks as though using a club (so +2 proficiency, 1d6 damage, instead of +0 proficiency, 1d4 damage.) Note that the Ruthless Ruffian rogue build can use clubs for sneak attack/rogue powers, if you are interested in sneak attacking people with pillows (or any other improvised weapons).
3) Weapon Master, a heroic feat in the recent Class Acts: Fighter article, requires having Weapon Focus and Weapon Expertise in one weapon, and lets you then get the benefit of those feats when using any weapon. (Alternatively, you might just be able to take 'Weapon Focus/Expertise: Pillow).
4) If you multiclass Barbarian, you can pick up Improvised Missile, which lets you use improvised melee weapons as heavy thrown weapons, and gives a +2 feat bonus to attack and damage when using them in this fashion.
With several of these combined, you can make a pretty effective build using any improvised weapon desired. Rogue multiclassed into Assassin (or Monk, when there is a Monk multiclass feat) has my vote, which both gives you good damage, and a nice selection of skills for making anything from a drunken master chucking ale mugs at people, to a little girl who beats people up with a pillow...