You can view and edit your Tinkercad design in the "Blocks" editor and configure the block size and material before exporting it for Minecraft.
In the editor, click the "Blocks" editor (pick axe icon).
You can change the materials for each object as you would like them to be in Minecraft. Just click the material to change it.
Click "Export" to export your "blocked" design to a SCHEMATIC file (.schematic).
Then, you can import the SCHEMATIC file into MCEdit (place it in your schematics folder) to place in your Minecraft worlds.