At first, I was going to recommend that you make a stencil of the design with an x-acto knife, and press it againts the cake and brush in the icing. But, it would probably take a long time to make the stencil.
If I remember correctly, Maid of Scandinavia/Sweet Celebrations used to sell rice paper that you could draw on with food marke (or food coloring or icing), and then place it onto the cake. The rice paper would dissolve into the cake, leaving the coloring on the surface of the cake. I have never used this product (if it still exists) so I don’t know how well it works.
Another idea would be to cut out paper templates of big shapes, and then use them as guides to cut out pieces of fondant or marzipan. You would then place the fondant or marzipan on the cake, and pipe in the dots. One drawback is that some of the shapes get pretty thin in the middle, and there is risk that the marzipan or fondant will break when you try to move it.
Good luck! It is a pretty design, but it looks like a challenge to execute.