I am about to put down a 3/4" oak floor in my dining room and hallway. My problem is, I am not sure what to do about the molding. My concern is that if I remove it and put it back down after I have the floor in, the height will be different when it meets at the corner of my other rooms. Should I just leave the molding in place and put quarter round down? What other options would I have? Any advice would be greatly appreciated.

This is usually hidden by either angling the base on the transition wall or shimming the base on a shorter wall or cutting down a piece until you get to an inside corner. .

in other words taper, shim , or undercut the difference until you are back to good. I would forgo quarter round though If you moulding profile might look better with a base shoe (some do IMO) then use it.