I'm out of my element because I don't have front loading laundry appliances and my TT doesn't have a laundry. Are you planning to purchase a gas dryer? If you are thinking electric dryer: Do you know if you can purchase a full-size dryer that has a heating element that operates on 110V? A quick Google on this showed primarily compact dryers which operate on 110.
With the washer I would wonder about water heater capacity. I guess a front load washer uses less water than a top loader but how many gallons of hot water do you need to run a load in a full-size washer? Another quick Google indicates the front loaders use 20 to 25 gallons of water per load. So you may get by with 6 gal of hot water on an individual warm cycle since there would be some cold water mixing in to make up the 11 gallons or so used per cycle.
Is your trailer equipped for a laundry? If not, are you prepared to install electrical, plumbing, and venting necessary to accommodate these?
I know I didn't give you answers but these seem like the things you need to understand to determine if this is feasible.