My guess would be a 12" square and an 8" round. HTH
ATo me, from the size of the golf ball on top it looks to me like a 10" square and a 6" round.
It seems like a 6 round and 10 square to me as well.
I did a search for the cake stand and the smallest dimensions found were 14" square. That is not to say someone else may be able to find that particular stand in a smaller size. That is the reason I thought the cake looked like a 12" and 8"...but, since you are the baker, you can make the cakes whatever sizes you choose! Yay!
Have fun making the cake; it is a wonderful design! And be sure to post a photo of your finished work!