Anything is doable, but note the fact that loading dishes from your sink into your relocated dishwasher will no longer be as easy as it is now. (When the penninsula's dishwasher is open, you'll be penned into that corner on 3 sides!)

Also, it appears you already have seating available just 2 feet from the proposed penninsula. Will you be moving that? Otherwise, there doesn't appear to be enough room between those two seating areas (penninsula & table) to get to the slider.

Your peninsula will need to be 40-42" deep--1" minimum front counter overhang, 24" deep cabinet, back panel/cabinet skin 1/4"-3/4", and 15" seating overhang (NKBA recommended minimum at counter height). I like the idea of a peninsula, but you should put a cabinet between the sink and DW, to give yourself a place to stand while loading. An 18" trash pullout would work well, with a 27" cabinet facing the back of the peninsula. How much space do you have for the width of the peninsula? 3" plus 18" plus 24" DW plus 2-3" return panel = 48". Or you might need a DW cabinet to support the counter top.