Well, Java's not a huge part of this issue in the first place. Unfortunately, that driver only supports OpenGL 2.0, which is a little old for our purposes, and doesn't seem to have any updates to give it higher version compatibility.
Minecrafts Vanilla system requirements state OpenGL 2.1 minimum to run the game. Unfortunately, I just don't think your rig has the power to really handle this stuff well, the older versions would be causing a slowdown, but if its hitting 1fps, its pretty much struggling all around. I'd love to recommend the standard "Try updating the graphics card" Approach, but I can't seem to find drivers for it anywhere. http://support.amd.com/en-us/download <-- May be able to auto detect your card and attempt an update on it, if anything is available.
Chefsbrian's post in Tinker Table causes huge FPS drop was marked as the answer