Yup, shimano axles are 9x1mm, if I recall correctly. Just about evry bike shop should have a replacement axle. And yep, undo the locknut, the conenut, then the axle and bearings will pop out, and replace the axle.

Is this a front hub? It's slightly more complicated with a rear hub, but both are pretty straighforward.

If you are at all familair with cone adjustment, this will all be very simple. Here's the instructions for a bearing rebuild:
http://parktool.com/repair/readhowto.asp?id=105