Using a rod down the middle is often false security
It *might* help some but don't depend on it. Making perfectly sure the cakes are perfectly level is the best security there is. Next, is using a dependable support system and those size dowels are SUPER strong.
If *I* were making this arrangement I would be using plastic drink straws in all but the lowest tier - and maybe even in it
I have used them sooooo often I cannot think of not using them.
The more I think about this the more I realize this cake is going to be 14" tall (7 layers 2" each) by 8" wide. It is going to be top-heavy no matter what! It almost would be better to use one long PVC pipe (2" wide?) glued to a base board and push/thread the cakes over it - you know like we so them doing so much on those TV shows - instead of the dowels in each tier.
I hope it does not need to be transported.