I didn't turn off the monitor until my boys were old enough to stay in bed and sleep through the night in a toddler/"big boy" bed. I guess that was about 3 years old. We lived in houses where the kid bedrooms were on the opposite side of the house from the master bedroom, so I wanted a way to keep "an ear" on them, so they wouldn't play all night and be trolls the next day. Also, I wanted to make sure they were old enough to be able to race down the hall to my room if they needed me. Once I knew they could do all that, the monitor disappeared.
Since neither son was observant enough to notice they HAD a monitor, I never suffered the "MMMOOOOOOOOMMMMMMY!" scream through the monitor. They just thought I was supermom who KNEW when they were 1) in trouble, 2) needing help or 3) on the verge of making a very poor choice! Too funny...
Use your monitor until you're comfortable not listening in at night. For some that's very young; for others, it's much later. I don't think there's a better or worse time.
Good luck!