I think the proportions you give are right, assuming that the biggest tier is 12" and not actuelly larger. Of course, the actual sizes you will end up using depend on the number of servings you need.
Well, I take a guess...I think the tier heights are 4-3-4. I really don't think the bottom one is 6 inches tall. And the difference of the middle tier was not necessary intended. As for their diameters, proportionally it looks like second tier is 4 inches larger than the top, and the bottom is about 3 inches larger than the middle. So based on that, the cake is probably 6/10/13. Just a guess... That design will look good in several different sizes depending on how many you need to feed.
Hope this helps.