I cracked one of mine after bottle conditioning for only two weeks and two days in the fridge, just to see. It was beer, but it seemed thin. I wouldn't say watery, because it had plenty of flavor, but it just didn't fill my mouth.
But after three weeks bottle conditioning and another week in the fridge, the beer had more head, more body and fills my mouth. The same beer, the only difference being more carbonation time, but we don't choose to drink flat beer for a reason.
If you only brewed a gallon, do yourself a favor and give that beer a couple of more weeks or you'll have it all gone before it gets really good.
Also, only keep a sixer in the fridge at a time, leaving the rest of your batch to continue conditioning at room temperature.
Primary 1: Empty!
Primary 2: Raging Red Irish Ale
Primary 3: Tasmanian (Galaxy) APA
Bottled/Kegged: Grateful Dead Guy, Bourbon Barrel Porter, Tasmanian APA, Oktoberfest, Maibock, Barnyard Brown Ale, Tasmanian APA batch #2, EdWort's Robust Porter, BierMuncher's Centennial Blonde, Mosaic APA, Moose Drool clone plus