Nope, anyone can craft, from level 1, no skills required. You only need skills to craft beyond level 15 (level 15 items I mean).Is it possible to have an alt level 1 to be crafter? Or you need levels to be able to craft?
Blacksmith/Clothier/Woodworker (make efficient use of racial motifs!)
Alchemist/Enchanter
Provisioner (lots of mats to collect for this one profession)