IDK ~ when mine were home alone, they were contained to a small spare room, which was baby gated so they couldn't get out.
They didn't get FREE run (alone) until they were 1.5 years old....
At 4 months, I'd say keep her contained, as they DO regress....
Best Wishes
P.S. Mine DID peel the paint off the walls ~ Actually they started to chew on the moulding, the door frame and furniture legs (in that room they were contained to)...So I had to get a whole bunch of USPS priority mail boxes (bc they were free) and open them up to and tape them together to make a "chain of boxes" to line the walls in the room to stop them were chewing on the walls...Then they started to chew on the cardboard boxes, so I had to cover it all in fabric - hahahahahaha ~ don't miss those days....
...just wait until the day you come home to confetti (chewed up pee pads) hahahahaha ~ definalty don't miss that!!!