Hi, I'm remodeling my basement, and installing a bathroom (sink and Toilet).This involves busting up the floor, which shouldn't be too bad since I will be tapping in to an existing pipe next to a main stack, within 6 feet or so of where the bathroom will be. Do I have to vent this separately? Or will that stack act as a vent?

" Do I have to vent this separately? or will that stack act as a vent?"
Yes and no! Yes, you'll have to vent off the lavatory and no you may not use the soil stack as a vent. It's against code and good pumbing practice.
But there is a bright spot. Instead of running the vent all the way to the roof you may use a AAV (Air Admittance Valve) "cheater vent" off the lavatory. Connect the lavatory drain to the toilet drain so the toilet will be wet vented. Good luck, Tom