jersey license runs out on december 31. federal and state stamp last til summer 08. so you'd have to buy a new license to hunt the 08 portion of the 07 duck season, but keep the old one with the state stamp and federal stamp. it's a pretty stupid system, and the first of at least 10 states i've hunted in where it's that way, but it is.
as for the hip number...i don't know. i assume that it would run out AFTER the season, like the state and federal stamps. but i'm not entirely sure. when you buy your license, whether from an agent or online, the agent or the site should prompt you if you need a new hip # to hunt the remainder of the season.