And I'd dowel down the center if it has to be transported already put together!
I would definitely.. even a cake board under your 6 inch would work too.. help to keep it collapsing your bottom layer... jodief is definitely right if transporting.. I transport my cake layers separate for this very reason.. the only ones that leave me assembled are 3D ones in which I use a styrofoam base under the layer of cakeboard, to my dowel some extra sticking power!
I think a cake board would work great under the 6 inch, but you could use large drinking straws to support it underneath and just dowel one large one down the middle so that it goes through the middle to support both cakes.
I personally have done 6 inch on top of a 10 inch and mine did not have to be doweled. I didn't use a loose filling, just BC and not a huge amount. It just depends on the filing and how heavy that top piece will be once completed. Mine were fine!
Hope that helps!
That is my most popular sized cake that I sell for birthdays. I always use 4 dowels in the 10", a board under the 6" and a dowel running through both cakes. Customers carrying a cake...not usually has careful as we are...especially if the dh picks it up! 
I just wanted to add that I doweled through 2 tiers for the first time last night. I sharpened the dowel with a new pencil sharpener and got out a small hammer. I was really afraid it was going to be hard to push through without a lot of pressure, but it was SO easy! Don't be afraid to do it!
Yep...that's why you hammer it....so it goes through the cardboard cake board and into the cake board on the bottom.
I had filled my cakes with strawberry mousse and it had to be transported put together, so I wanted the dowel to help prevent any possibility of sliding.
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