With our son we did 3 months...with our daughter we did day 8~ lol...she sleeps much better in her own room and sleeps longer! My son was scared of being alone so it was a tough transition for him, I wish I would have done it earlier!
She wouldn't sleep longer than 30 minutes in the PnP in our room, so she moved into her own room right away. Sucks because her nursery is upstairs and our room is downstairs, but now shes sleeping longer so its getting better.
I don't think there's a specific age, but I want to move DS to his nursery before I go back to work in 5 weeks. I feel that at 3 months it'll be a lot easier of a transition than at say 6 months. Right now he's still waking up every 2.5-3 hours at night to eat so it's just easier to have him in the PNP in our room.
I'd say when your LO is sleeping longer at night, when anyone's sleeping is being interrupted too much, or depending on distance from your room. With my girls I moved them at 3 weeks and 6 weeks, because their bedroom's were a room away.
Re: moving LO to own room?
I felt the same way. It's been one week of crib sleeping for us, it took 2 1/2 nights on the nursery floor for me.