It depends upon the type of pipe you have for the supply and drain such as copper, cpvc, or galvanized among others. If copper can you solder connections? With the wall exposed, this is a reasonably quick and cheap job for a plumber to do the water supply lines. The drain will have a vent going up and moving it will depend upon access and if it is galvanized, pvc, or abs or even copper. Anyone with reasonable diy skills can learn and handle pvc or abs.
I'd suggest you find the finish floor height and fit the pedestal up to the plumbing to see if if will cover it or not. They have a narrow base and neck and then widen out to the bowl. You also have to have room for the trap and tail piece below the sink which is why you don't have much leeway. Better to find out before you install the wainscoating. Also some pedestals don't fit tight against the wall and you can see the plumbing behind them but I don't know what type you have.
I personally prefer vanities. Just think about where you are going to put all the stuff that normally collects on top of vanities from daily use(I'm assuming here) and then decide if everyone can change their morning routines to put up the hair spray, hair dryers, combs, brushes, toothpaste, toothbrushes, makeup, contact solutions, etc. they use. The pedestal sink isn't supposed to hold that stuff and may be more cluttered than you are now. It may involve a lifestyle change that won't stay changed very long, like going on a diet. I guess I don't live everyday like the houses they have prepared for those photo shoots in Martha's magazine which really look nice but unlived in.