I spent a couple years delivering appliances. Appliance dollies are great, but I still wouldn't use one to climb hardwood steps. Those little stair-climber rollers can leave dents. You have to be extra careful with a metal blade not to let it even TOUCH your floor. And the wheels are hard and solid (for heavy loads) so they are tough on floors as well.
Seriously, for just a washing machine, I'd lay out an old blanket on the steps. Then lay down a layer or two of cardboard (from the washer's box) and lay the washer over on it's side. Push up the stairs from the bottom, while having your wife above just to pull the blanket along and keep it from getting hung up. It'll slide easily, and no damage to the floor. Use the same trick once you're upstairs - stand the washer up on top of the cardboard on top of the blanket and slide it wherever you want it to go.
