Have a think about the hot and cold for the washing machine. Seemingly washing machine use very little from the hot supply, the usually just fill up the pipes from the hotpress to the machine rather than the machine. You may only need cold which is simpler plumbing. having the washer and dryer beside each other is handy though.
If you already have a vent for the dryer I'd tend to leave it in place, unless you could move both under the stairs and have a real utility. My house has washer and dryer under the stairs and they both fit lovely.
Is there anything else you can move from your kitchen to make place for the dishwasher? Maybe one of the normal cupboards could go?