You don't HAVE to pull the carpet. The wainscoting doesn't HAVE to go clear to the floor. Infact if you are not wanting to replace the carpet right now, i'd leave it up enough to pull the old carpet. The baseboard should go pretty tight to teh carpet.
When I install baseboard in a house and the painter, carpet layer and myself are all on tha same page, I isntall baseboard BEFORE carpet, about 1/2" above the subfloor. Paint it in place, then the carpet layer can tuck the carpet right under. Saves alot of hassle masking/ cutting in paint against carpet.
The IDEAL way to install wainscotting is to cut the sheetrock back, add nailers(and possible more insulation on exterior walls) then the wainscoting, then chair rail above and baseboard below, as a way to aleiviate the sticking out into the room problem.
Just my humble advice. Worth every cent you paid for it!