With our icing recipe and by optimizing the print speed, each new layer prints while the previous layer is still semi-soft. Ideally, you want to set the layer height so that you get the new material pushing in a little to the previous layer. This ensures good contact between layers.
Royal icing is a little different from store-bought icing. Royal icing is designed to harden into a more candy-like structure. This, combined with 3D printing, can allow for lots of interesting objects to be made that would be tedious otherwise. Our recipe modification retains the self-supporting nature of royal icing for printing multiple layers.
As for slic3r adjustments, you would set the layer heights for about 0.5 to 0.75 times the nozzle diameter. We usually used a nozzle no smaller than 0.84 mm. Make sure the flow rate is ideal enough to allow you to print at a speed of about 15-20 mm/s (a print speed much faster will give you whiplash effects in your print).
If you are just starting with this, try an easy, flat object first -- something like a simple logo that goes up to maybe 10 layers thick. This will help you get a feel for this kind of printing before you try more complicated items.
Happy to help if you have more questions!