I have made a cake like this and had it sitting on a glass plate. It was four tiers high. I didn't have a cardboard piece between the two, and it worked fine. Drove 40 miles with it on my lap and it worked. I did glue the cake to the plate with frosting though, so I think that helped.
I think doing it this way is kinda at your own risk...
I don't really know of any other way to secure the cake, I've added two dowels before just because I wanted to feel safe about it. Also, there's an article here on cc about a different way to make a crooked cake as well...but, I've never had a problem doing it this way