Do you mean a character designer, like making concepts or a character modeler, where you get a design and then model?

If its the latter then I would say, modeling and texturing would be your main things to go for. With a good knowlage of rigging as well.

There was a nice quite indepth tutorial in last months (think it was that) 3d world about creating a dino beast, well worth looking into as it goes over reasons why you need to know the whole process, such as modeling for animation and how making a little test rig will help out in the modeling before going further in the pipeline