Hmm... currently I've got the *.blend file set up so the material, texture and image name (datablocks) are all using the same 'name', "bunnysneaky", which is the same as the file itself "bunnysneaky.tga". That image is loaded using relative paths so it appears in the "Source:" block as "//bunnysneaky.tga".
The mesh is exporting but in the md3 viewer applying a skin or an actual texture image just renders the object black, which usually means there's a texture loading issue somewhere. Now I can't quite remember if the texture image datablocks in Blender are supposed to reflect the 'shader' path, meaning the text fields (Texture > Image > datablock ID) should be written as "/models/path/texture" and not just "texturename" because the script gets the actual pathing info from there, or at least it used to?.