Wow after reading about what other moms have said, I feel like a bad mom. LOL. My daughter started playing in her room around 18 months. If I couldn't hear her I would check on her; usually meant she was up to no good. There is/was nothing in her room that she could pull down, climb on and tip over or any other 'danger zones'. Her dresser is in her closet, which I can lock. I now let both my kids, 4 and 2.5 play in their rooms together or separate as long as they want. I encourage them to play with just each other or by themselves.
As far as baby monitors. I couldn't sleep with one on because I would hear every movement of my children! Our bedroom is in the basement and the kids are upstairs. I stopped using the monitors when my kids were 6 months and 24 months. Both of them were sleeping through the night and if they woke up and needed something, they both could cry loud enough for me to hear them.
Do whatever you feel is comfortable. As far as the room, I'm sure your child will find something that you didn't babyproof, for me, it was lotion.... Live and learn:)