As soon as you have trained for Artisan you will need to move on to a zone will level 40 beasts. A good place to skin in wow is Thousand needles. Head to the western edge of the Shimmering Flats and look for Snakes and Scorpions to skin. You may want to stay at Dustwollow Marsh if you want or if you have more quests to complete. But you will need to finish your skinning training at Thousand Needles as there is much more beasts to skin there. From here onwards you will need to continue your journey from thousand needles to Tanaris and then Un’Goro Crater to reach the minimum level of about 300 before you can head to the Outlands. You will be able to skin Heavy Hide from these areas as well.
To learn Master in skinning you will need to be at least level 275.
Dustwallow Marsh (175-220) (level 35-40)
1. Mudrock Spikeshell, Noxious Flayer
3. Searing Whelp
4. Scorchscale Drake