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No, buying a new disc will not help. The problem seems to be that the connection with how the disc and the hub mate is loose... it's very similar to having a loose hub. I would definitely have your LBS take a look at it, you could develop wear in that area and cause all sorts of other problems. If you are trying to take care of it yourself... then you'll need to pull it all apart and tighten everything. Let me know how it goes!
I have already taken it to bits and tightened everything, with no effect whatsoever... There is simply too much air in between the disc and the hub, and I can't really see how that can be mended - unless I get a hub and a disc that fits snugly. I'll see my local bike repairman about it and let you know what happens!
It will be interesting to see what your LBS finds. It almost sounds as though you are missing a spacer, if you have that much room. Time will tell:):)