Prepare the grill for direct and indirect cooking.
Once the grill is hot (you can hold your hands an inch over the grates for no more than 2 seconds), stretch and shape the dough into a 12-inch round on a flat surface. Brush the top with oil and toss on the grill, oil-side down. Cook until the bottom is golden brown, 1 minute. Check the bottom of the dough to see if it is getting browned. If it is on one part, but not the other, use a spatula or tongs to rotate the dough 90 degrees and cook for another minute. If it is still not beginning to brown, cover the grill and continue to cook a minute at a time until the bottom has browned evenly. (It should only take a couple minutes if you have a hot grill.) The top of the pizza dough will also start bubbling up with air pockets.
Once the pizza dough has browned on the bottom, flip over and grill until golden brown and the dough is just firm, another minute or so. Remove to a sheet pan. Cover the grill so it retains the heat for the next step.
Combine the mascarpone cheese and honey. Smear the mascarpone over the pizza and scatter the plum wedges and berries on top. Put the pizza on the sheet pan back on the grill, close the cover and cook just to warm the fruit, about 2 minutes. Dust with confectioners' sugar and serve immediately.