dowel rods are used to support a second tier of cake, i.e. two or more complete cakes that are stacked on top of each other. A single layer cake measuring 2" (or even a torted, two layer cake totaling 4" ) would not require dowel rods.
heating cores wouldn't hurt. i usually use upside down flower nails on large diameter tiers.
chill the cakes well (overnight or for a 4-5 hours) to make the cakes easier to fill, frost and position. I wouldn't flip a cake that size onto its base to assemble. I would slide the cake off of a cake board and onto the filled base layer.