Go to Stranglethorn and start questing, it has the largest amount of animals to skin, that i have seen, and there are plenty of quests to get you past level 40. I would suggest what the poster above said, tag along with someone. It will not work as well with a hunter though. When I was level 14 or so, I played healer (I am a druid) to a rogue buddy of mine in the Wetlands. I was easily able to level up my skinning by doing that. Another possibility is to offer some skins to people helping you so that you can skin. If they are skinners, they will appreciate the leather, unless they need the skill ups as well.
I would stick to Stranglethorn for now, until you level up enough to go elsewhere... There are so many people questing there, that it is easy to follow someone and skin the animals they kill. A few quests will actually have you killing these beasts, which helps out a lot. The hunter camp has you killing the tigers, panthers, and raptors in the area, and there are always people working on them. Right now, it is not really necessary to level up your skinning too much right now.
Hope that helps