I just starting playing the game and don't know what to do. I'm a leek 6 night elf hunter. I finished all the starting quests. Should I leave the little night elf island that we start on? If so, how? Should I take quests on the island or what? Please help!

You should level up to 11 before leaving Teldrassil. If you finished all the quests in your starting area, there are plenty more where that came from.

When you've finished the low level quests at Shadowglen (Night Elf starting place) follow the path out of Shadowglen. There will be a quest at the gate out of Shadowglen. Start it. It will tell you to go to the town Donalaar or something. You will find Donalaar when you keep following the path. Once you're there, there will be heaps of quests for you to start. Don't forget to make Donalaar you home.

To get out of Shadowglen, go to the big house, and there should be a stony path. Follow it.