I have never shut the bedroom doors. Too paranoid.
When DS was sleeping through the day in our room I'd pull it, but never shut it & only coz our brm is right next to the lounge room.
Both my girls went into a big bed at 13 - 15 months.
Neither of them wandered. If they did it was dark, so they came into our bed. DD2 still does sometimes & DD1 will usually just go on the lounge.
They've never done anything else though.