You bathroom and your laundry traps will all require venting beyond that of a 1-1/4" vent.
I'm not sure what you are referring to by "the stack". The new bathroom drain connection will need to be made to the horizontal building drain under the floor, so where the existing stack is located is irrelevant.
The water closet can be wet vented by the lavatory's vent. The shower will need a vertical vent take-off upstream of the connection to the main line.