FTM with a weird question

Just sitting here thinking of any and everything... lol... I know nothing about taking care of babies other than the class I took and YouTube videos I’ve watched. I’m honestly not worried though, I already feel that motherly instinct.

Anyway, my question is when baby naps during the day do you always have to be in the same room? We have a small house and no monitor. But I would like to workout and run on the treadmill in our home whenever the dr clears me. Can I let baby sleep in the next room? Or can he sleep in our gym room while I run?